I have been told that I can't say "I hope I get this job (for example)", instead of it I should say "I hope I will get this job". Here's my question: does it make difference (cuz I feel like it does); and if yes, what is it?
There's been a significant usage shift in this area over the past century or so. Consider this NGram...
To the extent that there might be a shade of difference between including the explicit "future" indicator will or not, I'd say we're perhaps slightly more likely to include it when there's some "distance" between the speaker expressing his hope, and the (later) time when the addressee has a (positive or negative) reaction. So you might think including will is more suitable if you're writing a note accompanying a gift being sent through the post, for example. But most people wouldn't think of or notice such fine nuances.
Note that this issue only applies to a few verbs (hope being one of them). With other verbs, such as I know / expect / think / etc. [that] you will get the job, the word will must always be present.
To hope means to wish for something to happen - and since you wouldn't hope for something you already have, that something is of course going to happen in the future.
It's redundant to include will, but not incorrect.
Extra words like this can serve as emphasis, or to provide less chance of being misunderstood if the listener isn't paying attention, etc., or to maintain rhythmic cadence in a song, poem or speech.