is it normal, that palms roots are above ground? - That is perfectly normal for a palm to do this. Nice spindle!

what do you do, when it looks like a branch is forming? - Your spindle is going to flower then set seed.

does one trim that looks like seeds to me? - You can trim the flowers and seed off without hurting the palm.

It is normal for palms to get above ground roots at the base of the trunk. Some species get more than others.

That "branch" growing out is actually an inflorescences (flowering structure). It will eventually open up out of a sheath revealing the flowers. That is a Spindle Palm, Hyophorbe verscheffeltii.

The other palm is a Pygmy Date Palm, Phoenix roebelenii. That is an inflorescence but it doesn't appear to have any fruit/seeds forming. It also appears to be somewhat deficient. Use a good balanced palm fertilizer on it, one with micronutrients included.