If my cousin gets married am I now related to his new wife's immediate family. Would I be related to his new wife's brother or sister?
The apparently simple expression related to actually hides an extra-ordinary amount of complexity. It might refer to any or all of the following
- a blood relationship (now better described as a genetic relationship)
- a legal relationship
- a cultural or customary relationship
In particular communities, each of these could impose familial obligations or limitations (taboos).
The fact that your cousin marries does not create any new relationship (that did not exist before). That appended caveat is necessary because it is possible that a search back through 10, 20 or more generations will show that you and the bride's family have a common ancestor (or two). We all have many more related family than we are aware of.
Obviously these vary across jurisdictions and time, but if we adopt an anglo-centric world view then we can confidently say that the Anglican (Episcopalean) Church sees no legal impediment to you marrying a sibling of your cousin's wife (subject to you meeting the gender requirements). You do not have a prohibited degree of affinity.
In many cultures, this is a rich area for linguistic study. In the anglo-saxon world we are largely restricted to the term cousin. Its strict usage refers to someone with whom we share a common ancestor although the word is now used to serve many other purposes (such as the all-to-common references to cousins-in-law).
Your questions takes on new meaning when (if) the happy couple have children. Your cousin's son is also your cousin (although one degree removed) and so the bride to whom you are now unrelated will become the mother of your (new) cousin. Try not to think about what happens if she were to ask you to be the child's godparent.
None of this technical discussion is of much practical assistance when you are all present at family (or is that, families) gatherings and wondering what to call people. Feel free to adopt whatever usage is acceptable to both parties and avoids confusion. Just do not say it in front of a genealogist, we tend to be a bit possessive of our vocabulary.
No, you would not - the term "cousin-in-law" refers to either your cousin's spouse, or your spouse's cousin(s). Neither legal nor anthropological/sociological affinity recognizes relationships more distant than that:
It's common, at least in some parts of the U.S., to refer to people being "related by marriage" as though the "in-law" affinity propagated indefinitely, but there's no basis for it other than popular imagination.