The first part of the question is straightforward.
- Is there any difference between "тоже" and "также"? Which?
The second one is likely to have a "yes"-answer, but anyway:
- From all the allowed places in a sentence, does putting "тоже" in different ones alters the meaning?
I better explain this second part with an example, for sake of concreteness. Do the following sentences mean the same? (I guess not)
- ты тоже танцуешь сальсу?
- Тоже ты танцуешь сальсу?
- Ты танцуешь тоже сальсу?
Maybe the second and third options have a clear meaning ("do you (like somebody else) dance Salsa?" and "do you dance salsa (as well as Tango)", respectively) but, in a context-free environment, so does the first one?
Optional question. Here is how the second question was originated. Once I was trying to socialize with three fellows: a guy, which we all knew was Russian, and two Russian-speaking girls. In order to know the nacionality of the girls I asked "вы тоже русские?". But what they understood was that I was introducing myself as Russian, while by saying "тоже" I actually meant "are you Russians too? (as the other guy is)".
- What should I have asked?