Mostly yes, when it means that you go to uni, that you study there. Unless it denotes some professor's scientific research, which is also possible.

Well... it can, but it changes the meaning. "X czy Y?" is clearly a sentence that asks to choose only one answer. This is what is generally used in such questions.

Imagine "Pójdę na studia albo do pracy" (I will go to university or to work). You cannot use "czy" here, because it's a declarative sentence. So you can use "albo" or "lub". Technically, if you use "albo", it should mean that you should only choose one of them. And using "lub" can allow you to actually study and work at the same time. But in reality, those two are usually treated as synonymous.

In conclusion: you could use "albo", but there's quite a possibility that your interlocutor will interpret it as a question that allows choosing both options. So I will add it, but "czy" is recommended.