Can someone use (for example) Psychokinetic Impact multiple times in one turn by splitting his potential into a +10 potential for each?

Maybe use the same power 5 times if he has a +50 Psychic Potential (no matter if successful or not)?

If so, what happens if he tries to hit the same target (for damage and/or other effects) with (for example) 5 uses of Psychokinetic Impact or any other (one or multi target) Psychic Power?

The most acceptable reasoning I got for why you could get multiple uses of the same power was:

" It is more like you have an amount of potential each turn and you can do whatever you like with it, much like Zeon on mages (they also can cast the same spell twice in the same turn)

because of the reduced strength of the power after a split it would work the same as with a single power if you target the same target multiple times"

This is correct that you can split your potential and use a power multiple times in the same turn, would never suggest doing it too much though unless it's for low level stuff and preferably with some of the level jumping advantages for powers. Personally though I have it house ruled that it's limited to a maximum number based on psychic projection just as attacks are. Saw a few too many fireballs flying around early level and making other characters obsolete as a result.

If you were splitting the potential, I would suggest not doing it evenly. Split it so you have 2 or 3 that just barely hit, then 1 that hits a lot harder. That way, you get the benefit of them have to defend multiple times.

Psycic potential has nothing to do with hitting.

that is where Psychic Projection is used for.

That is correct. What I was referring to is hitting the minimum potential level.

Wouldn't splitting the psychic potential that far result in a potential (and probable) massive fatigue, or unconsciousness? Psychokinetic impact requires a minimum potential of 80 (if I'm remembering right), so if you split 50 into five +10, then you need to roll a 70 or higher five times.

That is correct. You usually want to split only if you have a higher Potential than the base level of the power, or are willing to increase your chances with free PP. Someone with only +50 Potential will probably not be slinging around multiple powers.

I have seen this go horribly horribly wrong. There was a mentalist that could split her potential up and have it be more effective than just a single strike due to the stacking penalties of defending multiple ranged attacks.

Cryokinesis, Extrovert, ridiculous amounts of potential and she was shooting out 10 ice shards in a single turn hitting people about 80% of the time for over 100 base damage at level 2-3. On the occassion that she got an explosion, they became AoE's.

Ridiculous.

I have seen this go horribly horribly wrong. There was a mentalist that could split her potential up and have it be more effective than just a single strike due to the stacking penalties of defending multiple ranged attacks.

This is easily countered by a Nemesis user who has matrices cancellation, Matrices cancellation depletes the potential of any incoming psychic power and since this player tends to launch several low potential strikes they would all simply fizzle out harmlessly.