The first part of the question is straightforward.
- Is there any difference between "тоже" and "также"? If so, what?
The second one is likely to have a "yes"-answer, but anyway:
- When considering all the places one could put "тоже" in a sentence, does placement of this word alter the meaning of the sentence?
I can better explain this second part with an example. To be specific, do the following sentences mean the same thing? (I am guessing they do 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 nationality 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?