Receiving direct messages from God is commonly called prophecy, and, depending on the religion, prophets are extinct since hundreds to thousands years. I don't think any mainstream religion claims to have prophets today - there are, of course, various freaks, but mainstream religious communities never make such claims.
So your description - unless, of course, you can back it up with some sources that contradict what I said - appears inadequate.
http://today.yougov.com/news/2013/10/25/god-told-me/
Prayer is absolutely "telepathic communication to God" in at least one direction. Prayer is something you can do in complete silence, and God is still supposed to be able to hear you. In any other context we would call that "telepathy".
The other direction is not quite as clear, but clearly a lot of people believe it. Beyond telepathic responses, there are physical replies to telepathic requests, for example:
http://www.catholic.com/quickquestions/if-a-person-asks-in-p...
http://www.catholic.com/quickquestions/why-werent-my-prayers...
Note that the answers are not "this is bad and you should definitely not do it", but rather a simple command to trust that God or the lesser beings will do what's best.
Which one would that be? If the prayer were God reading your mind, you didn't need to pray - God is omniscient, so He already knows what you're praying about. Moreover, He already knew what you would be praying about before you started. Why they are praying then, you ask? Try to answer this question (honestly, not jumping to the convenient conclusion of "all of them are idiots that couldn't see such a simple thing") and you'll get closer to understanding what prayer is. If they prayer would be you reading God's mind - I don't think any Avraamic religion would adopt such blasphemy as a human reading God's mind and understanding it.
>>> and God is still supposed to be able to hear you
You realize you just assumed God is a human which needs sounds to communicate, right?
>>> In any other context we would call that "telepathy".
Really? I just communicated with you in complete silence, yet it wasn't telepathy ;) Moreover, I simultaneously communicated with thousand other people, and didn't have to shout very hard either. Obviously, I'm some kind of wizard or something :)
I think you'd not get very far if you anthropomorphize God and imagine it's just some bearded dude sitting on a cloud. I, of course, far from prescribing a religion to you - if you want to believe this is how the God is, feel free to. I'm just saying it's probably not what most of the Christians believe in.
>>> a simple command to trust that God or the lesser beings will do what's best.
So where's a divination in that? Where is the fortune telling? I'd say if one of the fortune tellers would tell you "hope for the best and eventually something good would happen" you'd not pay much for that. That's why actual fortune tellers are much more verbose. I wouldn't vouch for the value of any of the verbs, but at least you get what you paid for.
The second answer, btw, explicitly says prayers are not magic - they are not supposed to force God (or any other supernatural being) into doing your bidding (that's basically what magic is about). It says it is a statement of trust, instead.
1. Most if not all Abrahamic religions hold that you can effectively pray in silence and without doing anything besides thinking your prayer.
2. Prayer is communicating with God and communicating by pure thought is telepathy.
3. God is expected to reply in some way, and you're encouraged to look for and interpret the reply.
Can you elaborate exactly which one(s) you have trouble with, and why?
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.
"The president of the United States has claimed, on more than one occasion, to be in dialogue with God. If he said that he was talking to God through his hairdryer, this would precipitate a national emergency. I fail to see how the addition of a hairdryer makes the claim more ridiculous or offensive."
(Note: don't take my quoting of Sam Harris as an endorsement of him in general. I have no idea whether he's worth endorsing or not, having read essentially nothing of his beyond that quote.)
Looking at it from the outside, there's no serious difference.
My point about "aren't approved" is that many religions explicitly recommend divination, fortune telling, seeking omens, and the like, but only in a manner approved by that religion i.e. by doing so through their God, rather than through cards or animal bones or whatever. They do not universally discourage such behavior, though.