The word “to” in this phrase is slightly confusing because it is usually used to introduce a verb, as in “want to” or “have to”. Even though saying “I want to hear from you” is completely correct, “look forward to” requires a different pattern:
Obviously, “hear” is not a thing, so it wouldn’t make much sense to “look forward to hear from you”. The thing you are looking forward to is “hearing from you”:
The reason is that “to” is just a preposition here and has nothing to do with the infinitive, just like in “listen to”—you would say “I listen to singing” rather than “I listen to sing”, wouldn’t you?
As for the question whether to use “I look forward to” or “I am looking forward to”, some people consider the two completely interchangeable, but most find the phrase with “look forward to” somewhat formal and best suited for formal correspondence, whereas “to be looking forward to” is more informal and friendly: