This is a very common mistake!
So, don't worry. Here is the cure.
Ask yourself which one makes more sense: "look forward to it" or "look forward to do it"?
Chances are you know that "look forward to it" sounds more natural, because you've seen or you've heard others use it that way before. And, yes, with look forward to, you need hearing from you (NOT hear from you).
Grammar points
The trick is to remember that to can be either the infinitive marker or a preposition1.
You need a verb after the infinitive marker to (e.g. I want to swim this evening).
You need a noun after a preposition (e.g. She went back to the pool.)
It doesn't have to be a real noun, just something that functions like a noun. In other words, it's the object of a preposition, as it's traditionally called; or as defined a little more precisely (same link):
The prepositional complement is typically a noun phrase, but it may also be a nominal relative clause or an -ing clause. Both the nominal relative clause and the -ing clause have a range of functions similar to that of a noun phrase: ...
(emphasis mine)
In your example, to in look forward to is a preposition. Why? Because you can say look forward to something (e.g. He had worked hard and was looking forward to his retirement.) In other words, saying "I'm looking forward to it" makes sense.
And that makes you need a noun or something noun-like, i.e., hearing, not hear:
I look/'m looking forward to hearing from you.
1When the preposition to is used in a phrasal verb, some people call it a particle, but let's keep this post simple and use only the term "infinitive marker" and "preposition".) Here is a list of such phrasal verbs (ending with to). Some common ones, in my opinion, are look forward to and be used to. Another common phrasal verb (but not on that page) is object to.
Bonus
Here is a related mistake which shares the same cause of confusion: used to vs. be used to.
Remembering this may be helpful:
He used to live in Frankfurt, but he's not used to living in cold weather.
The first to is the infinitive marker to. The second to is a preposition.
The first to is about "He used to do something".
The second to is about "He's not used to something".
Best Answer
No, because all examples describe a future state. (Although in practice, neither would be viewed as inappropriate.**)
All of those examples apply to some possible future event (that, as you say, the speaker is thinking of doing or would like to do, i.e., hearing news, hearing progress, hearing proposals), so the formations as given can be correct.
If they were phrased in the past tense, interested to would be appropriate. For example, if the speaker had already heard the proposals, "I was interested to hear any proposals he might have had" would be a proper statement of his mood after hearing the proposals.
** The speaker could also be considered to be reflecting on a hypothetical future state, so "I would be interested to hear any proposals he might have," meaning "If I did hear any of his proposals, 'interested' would describe my mood" wouldn't come across as incorrect.