Yes. So-called "cousins by marriage" are not really related to you; you don't share any ancestors with them so for marriage purposes they are the same as anyone else. Besides, all states in the US permit second cousins to marry.
You haven't provided your jurisdiction but in most jurisdictions you can marry your third cousin.
Two issues here. Most places, being a second cousin is not an issue legally. Might be frowned on by the people around you, but that's their problem. Second, if you are of the same sex, do you live somewhere that it is legal for same sex to marry? It is not legal everywhere and even if you went somewhere that it is, that marriage will not be recognized when you return home.
If you marry your father's first cousin's son, you are marrying your second cousin. As recently as the early 20th century, in some ethnic groups marriage between even first cousins was accepted, if not an everyday occurrence Today, many people in the developed world frown on first cousin marriages and some also oppose marriages between second cousins as being between people who are too closely related. Marrying your second cousin carries less risk of genetic disease to the children than does marriage to a first cousin, and even then the risk, while elevated, is not usually huge and probably does not exceed the genetic risk to the child if the mother conceives when older than 40 years.
Certainly. Even first cousins can marry in about half the US jurisdictions and in many other countries. No place forbids marriage between third cousins.
No doubt some groups would call a second cousin marriage inappropriate or even sinful. However, many others would not.
There are no laws about dating. Most states don't have a problem with second cousins dating. It is even legal to marry a second cousin in most places.
No - in fact, it's not illegal to marry your third cousin anywhere. There is enough genetic distance between you and she or he that the old prohibition against marrying anyone close than cousins does not apply. And there is some evidence that even that concern is groundless, now that we know a bit more about genetics than we did in 1850 or so..
No. A prenuptial agreement is good ONLY for the nuptials (marriage) in the agreement. Once you divorce, the nuptials (marriage) in question have come to an end. Even if you marry the same person a second time, that is considered NEW nuptials (new marriage) and would require a new prenuptial agreement. Or you could marry the person WITHOUT a prenup the second time. It is up to the participants.
There are no restrictions or laws that would make it a problem to date, or even marry, a third cousin.
Yes it is legal to marry you fourth cousin in all jurisdictions. As a practical matter, most people don't even know who their fourth cousins are and so would not know if they were marrying such a cousin or not.
In many countries, including half the states in the US, it is legal to marry your first cousin or any other cousin. Most jurisdictions, even those that do not permit first cousin marriages, do not object to second cousin marriages. Some people believe that marrying your first cousin will increase the risk of having a deformed baby, but unless you both come from families with a long history of cousin marriages, the increased risk is actually very small. While cousin marriage is not uncommon in some groups (European 19th century royalty and eastern European Jews, for example) it is nontraditional in many cultures, and many family members may protest against such a move.
No, it isn't. Pennsylvania § 1703. Marriage within degree of consanguinity. All marriages within the prohibited degrees of consanguinity as set forth in this part are voidable, but, when any of these marriages have not been dissolved during the lifetime of the parties, the unlawfulness of the marriage shall not be inquired into after the death of either of the parties to the marriage. (e) Marriage to relatives.--No marriage license may be issued to applicants within the prohibited degrees of consanguinity which are as follows: A man may not marry his mother. A man may not marry the sister of his father. A man may not marry the sister of his mother. A man may not marry his sister. A man may not marry his daughter. A man may not marry the daughter of his son or daughter. A man may not marry his first cousin. A woman may not marry her father. A woman may not marry the brother of her father. A woman may not marry the brother of her mother. A woman may not marry her brother. A woman may not marry her son. A woman may not marry the son of her son or daughter. A woman may not marry her first cousin. § 4302. Incest. A person is guilty of incest, a felony of the second degree, if that person knowingly marries or cohabits or has sexual intercourse with an ancestor or descendant, a brother or sister of the whole or half blood or an uncle, aunt, nephew or niece of the whole blood. The relationships referred to in this section include blood relationships without regard to legitimacy, and relationship of parent and child by adoption.