1. Depends. E.g. see some Judaic takes on it: http://judaism.stackexchange.com/questions/7872/which-parts-... I'm sure there are different takes on this among Christians and Muslims too.

2. Not really.

3. Not at all.

The idea that you can make God do things by thinking about some stuff sounds strange to me. However, nothing I know about Avraamic religions suggests you can do that. Of course, the scripture contains examples of people - called prophets or Holy Ones, etc. - communicating directly with God and even causing change is God's behavior (the latter is exceedingly rare, but you could find some examples) - but a normal regular person is not expected to do that.

Let's take what I consider to be the most obvious part: #2. You say that communicating with God using pure thought is not "telepathy". Why not? Communicating with pure thought is basically the definition of the word.

I say that the claim that prayer is "communicating with God using pure thought" is your assumption which in no way actually corresponds to what prayer is. Pretty much the only part that is probably correct there is "God", all the rest is assumptions which might be true but usually are not. E.g., actual catholic links above say prayer is an expression of ultimate trust. Not the only definition possible but certainly doesn't fit what you're saying. Repeating it again, it is not possible to reach correct conclusion if you start with wrong assumptions.