I have a few questions regarding the Edo Period in Japan:
-Social Class / Social Obligations
-Religion/Beliefs
Lots of questions! I'll do my best, briefly:
-Social Class / Social Obligations
In theory, no. Social status groups were supposed to be largely distinct, but in fact there was overlap and some social mobility at the edges. Also, as the period went on, some merchants were able to buy samurai status or otherwise break out of their group.
In theory no, though it did happen. There are plenty of stories about tragic, doomed lovers from different social groups, which means it was part of the lived experience of many people during the period.
I'm not sure I understand what you mean by "choose to demote themselves." Rank within warrior society was not in your own control. A samurai could, however, join the Buddhist priesthood, or become a scholar, and thereby lose samurai status.
Husbands and wives ran the family business together. In theory the husband did the more public-facing work, like interacting with customers while the wife ran the internal part of the business, including managing the finances, but the actual breakdown of labor varied from family to family.
The business of the family changed depending on your wealth and social status. In a farming family both husband and wife might work in the fields. In a large merchant family the wife might mange the servants while the husband managed the business. In a mid-level samurai family, the wife might spend much of her time tending to the family's collection of textiles, mending clothes, and preparing family members for their service in the castle offices--how you looked was extremely important for samurai.
See above.
Wow, too broad for me to answer simply!
Sometimes, including "adoptions" in which a young man from another family would be married to the daughter and would thereby become the heir of the family business. But falling in love with someone without your parents' consent also appears often enough in plays and fiction to tell us it was a relatively regular trend.
You were born into the social status of your family, usually determined by your occupation.
Too broad. Can you clarify what you mean?
No, this was a highly patriarchal culture in which the power and pleasure of mean was paramount. People might have looked down on a man who consorted with courtesans but it was not uncommon for men to have multiple lovers--wives, concubines, and also younger male lovers.
-Religion/Beliefs
Oof. In the Tokugawa period, samurai were not able to fight wars, be rewarded for conquests, or compete on the battlefield. They became bureaucrats, and many became very poor. I don't think "the samurai code of honor" meant much at that time. See the historian Oleg Benesch's work on this subject: http://www.olegbenesch.com
This was a way of redeeming some semblance of honor in an otherwise shameful situation, such as after betraying your liege or loosing in battle.
Very rarely the "honor" of seppuku was extended to someone outside of the samurai group (see the suicide of the the master Sen no Rikyu in 1591), but usually this was just a samurai practice.