Alright, so a lot of your questions get to the very heart of why this case was so controversial, because those are the same interrogatives a lot of Pro and Anti-Slavery had. It's also because of this that they wanted the Supreme Court to give a definite answer - which the decision was not, intensifying instead of settling the slavery question.

Question 1: How? How was he able to lease another man in a state where slavery was illegal?

Sadly, something being illegal or immoral doesn't mean it doesn't happen, especially when there are no mechanism of enforcement. Often slaveholders simply ignored free soil laws, claiming instead a right to "sojourn" - meaning, holding the people they enslaved in free territories and states in a temporary basis. Several Northern states enacted laws to prevent this, declaring that as soon as an enslaved person set foot in their territory they were freed. But there was no such laws in the Federal territories, largely because of the pro-slavery bent of the US government as a whole, and the fact that even previous to the infamous Fugitive Slave Act the US had a constitutional obligation to return "fugitives". Southern soldiers and officers benefitted from this especially, often bringing their slaves to forts in free states and territories, even as far north as the Pacific Northwest. Without extensive enforcement of free soil in Wisconsin, and with a Federal government that was all too willing to overlook if a military man brought some slaves as a "right to sojourn", there was little Dred Scott could do except flee or sue.

Question 2a: How did he expect that to work out? What would prevent Dred Scott from simply running away in a free state?

Question 2b: Since Dred Scott already ran away once before, why did he not do so while he resided for 3 years in a free state, at times without his owner even present?

It's difficult to examine the motives and thought process of Dred Scott the man since most historians and people were and are interested in Dred Scott the case. It's possible that Emerson believed that Scott would be loyal to him, a delusion that a lot of slaveholders shared. More likely, he believed that the constitutional Fugitive Slave clause would return his human chattel to him. Even though it was rather ineffective (explaining why the South clamored for a stronger law), this constitutional recognition of slave property meant that a lot of Free States recognized the "right to travel" and would return escaped fugitives to their owners if captured. Those states that enacted Personal Liberty laws and laws that denied the right to sojourn were radical Eastern states. Illinois was not friendly to the enslaved, a lot of its people being hostile to abolitionists.

So while Dred Scott could have probably ran away again, his chances of success were slim and risks were high. If caught and remanded, harsh punishment was probably in store for him, and masters were not above punishing family and friends still at home. When Scott married a woman Emerson enslaved, the risks of fleeing were higher since it would mean separation from his wife, and probably exposing her to danger. When all this is taken into account, Scott probably decided it was not worth the risk, until he obtained the support of White friends in a less risky judicial way that would result in legal freedom, not merely physicial freedom that still exposed him to the risk of reenslavement.

Question 3: How could a slave have any of his own money, let alone that much money?

Though the favorite method of slaveholders for maintaining discipline and forcing labor was the whip and other kinds of violence, some masters, especially those who saw themselves as enlightened and good, allowed their human property to have "positive encouragement". Some masters thus allowed their slaves to work on their free time to obtain some money, a peculium the bondsmen were allowed to hold. However, there were no real legal protections for this peculium or any legal disposition forcing the master to respect it or accept it in case the slave tried to buy his freedom. Some masters accepted the peculium, others like Mrs. Emerson did not. I can't find how exactly Scott got the money. Maybe Emerson had allowed him to keep a peculium, or the Blows gave him the money.

Question 4: How could a slave sue for his freedom? What's to prevent his owner from ordering him not to sue or otherwise stifling his ability to do so with the no doubt considerable power she had over him?

Slaves suing for their freedom was actually not as rare as you might think. "Freedom suits" were a common method of obtaining freedom, and preferred whenever possible because it meant legal freedom, not merely a de facto one. Often, these were brought by the slave themself or by White allies, but Courts generally recognized the right of slaves to sue for their own freedom. Missouri's territorial code in 1807, and later its 1824 constitution, permitted freedom suits as a legal mechanism, so Dred Scott was exercising a legal right. Under these statutes, Missouri Courts actually granted freedom to several slaves who sued on grounds similar to Dred Scott's. Despite the legal validity of freedom suits, a master could probably then physically prohibit a slave from bringing forth a suit or threaten them to prevent them from doing so. In this case, the help of the Blows was vital to Dred Scott.

Question 5: If the Blows aided his legal defense, why could they not have spent that money to instead buy his family out and then free them?

Given the previous refusal of Mrs. Emerson, it's likely she would have refused, even if merely out of principle. Curiously, Mrs. Emerson's second husband, Calvin Chaffee, claimed that he knew nothing of the case and that both he and his wife wanted to manumit Scott. Some have even said that Sanford, the former Mrs. Emerson's brother, was never Dred Scott's legal owner. In any case, after the case was decided Dred Scott was deeded to Taylor Blow, who freed him and his family. So, one has to wonder, if Irene Emerson wanted to free Dred Scott, married an abolitionist, and after the case deeded him to one of the Blows, why did she refuse his attempt to buy his freedom? As far as I can tell, we don't really know.

Question 6: Why did Dred Scott not use his brief window of legal freedom to get the hell out of Mississippi?

Missouri you mean. It seems that Dred Scott, naturally, did not want to leave his family, who were trying to obtain their freedom through a parallel but separate suit, and that with the case still pending due to Mrs. Emerson's appeal, his freedom was not truly secure. I can't find if the Courts prohibited him from leaving the state, but in any case Dred Scott's possibilities were narrow. Without his family, barred from most states who loathed and discriminated against free Blacks, and with his case still pending. Fleeing would probably have exposed him to greater dangers, exposed his family as well, and would have worsened his legal chances for the Missouri courts would likely have declared him a fugitive. Reading the Missouri Freedom Suit Act, it seems that if an appeal is pending the enslaved person is to be held by the sheriff and be put to work to pay the sheriff's fees. I should note that after he finally gained permanent freedom, Dred Scott continued to live in Missouri.

Question 7: Why would she appeal the 1850 verdict if she married an abolitionist?

Indeed, why? As I mentioned, Chaffee claimed later that he didn't know of the case and that he and his wife both wished to manumit Dred Scott. This isn't consistent with her actions. Maybe Chaffee was defending himself from those who attacked him as a hypocrite saying he owned slaves at the same time as he talked against slavery. I can't find information regarding Irene Emerson's motives or opinions. But it seems that she had pro-slavery views in spite of her husband's anti-slavery ethos, the transfer of Dred Scott to her brother Sanford being an attempt to prevent Chaffee from freeing Scott. After the suit ended, Chaffee did indeed free Scott by giving him to the Blows, a necessary step because Missouri law only allowed state residents to free slaves there. Irene had no legal recourse since as a woman she couldn't hold property once married, but she did insist on receiving the wages Scott had earned, saying they were her property. This, is obvious, it's not something a real abolitionist would do. So it seems that Irene didn't want Dred Scott to be free.

Question 8: Why would an abolitionist marry someone who not only refuses to free a slave but even tries to keep him enslaved when even the slave state she lived in recognized him as free?

Again, difficult to know. Chaffee claimed he never learned that Irene was the owner of Dred Scott, said he wanted to free him, and indeed as soon as he could he deeded him to the Blows. Maybe some of this was merely to protect himself from criticism, and his later noble actions were to salvage his reputation and political future. Or he really didn't know, not realizing Irene was actually pro-slavery.

Question 9: What?? If they gave the Scotts away to someone who was obviously going to free them, why didn't they do it themselves? Why didn't they do it earlier? Why would they do it right after the highest court in the land gave them the strongest legal basis for keep the Scotts enslaved? What kind of abolitionist owns slaves for 7 years, even if he married into them?

As I explained, only Missouri residents could free slaves, so it was necessary to transfer them to Blow, who lived in St. Louis. While the case was pending, Sanford was the owner, though as I noted this is contested. After the decision, Chaffee did what was necessary to free Scott, claiming he never knew until the case reached the Supreme Court.

What role did President Buchanan have in the Supreme Court decision? I was listening to a podcast on the presidents that he pressured the court to not only find in favor of Sandford but to proclaim that people of African decent cannot be citizens. In the vain belief that it would solve the slave problem once and for all.