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I started with the hobby this week because I felt like doing something creative (and I have time). I've never painted miniatures, so I'm a bit lost.
After reading several tutorials and buying some tools and minis I assembled three hormagaunts (only the body, to keep the things simple) and applied primer (Skull White). However, I have two question with regard to my result: picture with two minis, one primed

I know that with the quality of that pic is hard to say, but, is the mini properly primed? The mini is not white, but kind of greyish, and it is not completely even.
I tried to remove the mouldlines the best I could, but although I wasn't able to feel the mouldlines with my fingers some of them keep slighlty noticeable (Is this going to have any impact at the end?).

I'm not sure whether I should keep priming until the coverage appears almost completely even and white, or it is not necessary? As far as I understand the main purpose of the primer is not to get a perfect coverage, but a surface easy to paint.

Welcome to the hobby!!!

You are correct in that when priming you do not need total coverage.

Now, the color of your primer can affect the color of your base coat, so sometimes I use a lighter primer for lighter colored minis - and in those cases, I use more coverage.

Yes, the primer exists to create a better surface for other paint to stick to (primer is chemically different than paint, and creats a surface paint sticks to).

If you have not, I would check out many of the painting videos on youtube, and other war gaming channels.

best of luck and have fun!