if i play an ultraball, start looking through my deck (but i don't quite remember my hand) , half way that i look at my hand, and then i try to finish the effect of the ultra ball, would i be permitted to finish my search?
Sure! But you should also state what you are doing. It never hurts to explain what you are doing.
There is an official ruling from Pokemon OP that a deck search is not over until you start to shuffle to deck at its completion.
