Fare baggage rules regarding tickets that are partially fulfilled by another airline

I am booking a return trip from the Middle East to the USA with a connection in the USA on the first direction, and a connection in Europe in the return flight. There are four flight legs in total, all booked through United. The first three legs are operated by United but the fourth leg is fulfilled by Lufthansa.

Questions:

1. Can two legs of a direction be of different classes when the same airline fulfills them?

2. If the answer to the last question is yes - can they also do it in that case? For example, if an airline on their most basic fare includes carry on trans-atlantic but only a personal item for domestic, and the first leg is trans-atlantic and the second domestic, they can just pull my baggage out?

3. Can two legs of a direction be of different classes when fulfilled by two airlines?

4. How can I check those details without directly contacting an airline representative? I checked on the websites but it's very vague. They tell you the class (economy k), but I read that Lufthansa, for instance, lists Economy Light as Economy sometimes.

I'm asking in a general way and not about those flights specifically because I often run into those questions and can't get a clear answer on the airlines' websites. Even the representatives give me vague/contradicting answers this time.