I'll try to address OP's questions.

1. It appears that slaves were a major investment and very capital intensive. Death or illness should have had a large economic impact on the process. Morals and customs aside, would it not be in the best financial interests of the slave owners to maintain the health and productivity of their slaves?

The bottom line is you cannot force people to work as slaves without violence or the threat of violence. It is the only way to maintain a productive labor force. More violence meant more production. The types of violence employed typically did not result in death, although sometimes killing was intentional and necessary if there was serious defiance. Slaveowners would maintain "health and productivity" as long as it helped the bottom line. Big profit margins required less concern paid to health and productivity. For example, on Caribbean sugar plantations, a slave would produce enough sugar in one year to cover his purchase price. The owner was now in the black. After this point it made economic sense to just work the slave to death and buy a new one. The average lifespan for slaves on the sugar islands was five years. Profit margins were slimmer for cotton, and slimmer still for tobacco and corn. Yet in all cases, physical violence was standard, and usually was employed in such a way as to boost profit, not cut into it.

2. Were the slave owners really so wealthy that they could kill something worth the cost of a modern car for no good reason? Even most modern wealthy people don't go around destroying $30,000 cars for fun.

Answered above. Sugar planters were among the wealthiest people in the world. Killing slaves was rarely done "for no good reason." It served to quell dissent and stimulate productivity. Irrational murder could happen where sadism and extreme wealth intersected.

3. Using slaves as security to back loans seems like very unwise collateral. A simple farming accident could render the security completely worthless. Present banks loan money on real security such as land and buildings which are obviously far more secure than a human life. Why would a bank in the 1800s even consider such a risky form of security?

Not only did banks securitize slaves, but planters bought slaves on credit. This seems analogously risky, since you are using that slave to produce a crop which will hopefully turn a profit allow you to pay back the merchant. Someone who knows more about financial history and the history of banking should chime in here, but antebellum America was suffused with financial risk. Lending and borrowing standards were loose, banks were not regulated by the federal government, and most investment was in agriculture, which is inherently risky, dependent as it is on good weather and international markets. (Edit: The futures market in commodities emerged gradually in the 1840s and 50s and didn't really take off until after the Civil War) (Edit #2: Railroad investment was tied closely to the future value of agricultural land.) There were major financial panics in 1819, 1837, and 1857. We might also note that bubbles occur nowadays too, even with "absolutely safe" investments like, say, real estate. On balance, slaves were a good investment during boom times because they would, usually, produce enough cotton (or whatever) for the owner to keep his head above water. If that didn't happen, the slave himself could be sold, and the value of slaves was more stable than that of cotton itself.

One solution to risk was the establishment of banks which allowed investors to mortgage slaves and borrow against them, up to half the value of your investments. Then you could use this borrowed money to buy more slaves, borrow against those slaves, and build a nice big pyramid. It was a safer and more flexible way to use slaves as collateral. The bonds issued by these types of banks circulated throughout the US and Europe, and by purchasing these bonds you could invest in the slave system without personally owning a slave, who could, as stated, become injured or killed or self-kidnapped.

4. In the event of a default, were the foreclosures or repos on slaves? Would the bank come and take the slaves if payments were not made on the mortgages?

Yes, this happened often. Then the bank would sell the slaves. If a master died in debt, slaves were both liquid and valuable, and would be very frequently sold under these circumstances to satisfy creditors. This would often require the break-up of families. Even benevolent masters might find themselves in deep debt.

5. After the abolition of slavery, I assume that the value of the security dropped to zero. Were there massive defaults? Did it bankrupt many once rich and powerful families and companies? Or, did the banks and financial institution simply write off the losses now that their collateral was worthless?

I can't answer this one. The first place I would look for an answer would be Edward Baptist's new book, The Half Has Never Been Told, whose previous work is my main source.

A component of beating or killing a slave was essentially to scare other slaves. Troublesome slaves weren't disappeared into the night, they were punished in public. As already noted, slavery doesn't really work without violence, or the threat of it. Otherwise your slaves won't work (as there is no incentive for them) or they will leave.

A credible threat needs to be demonstrated, especially if the 'rules' are broken - otherwise people stop taking the threat seriously and they see how far they can push their luck. A modern example of credible threat and perception lies in the nuclear arms race - the other guy (in theory at least) had to be convinced you were serious about using your arsenal in order to achieve deterrence.

In this way punishing a slave does make sense - the potential for violence is demonstrated, the other slaves now (hopefully) don't need to be 'reminded' again and work continues as desired. The brutality of it might actually enhance the impact and hence the effect on the 'audience'.