Yes, "still" is a good word for "wciąż" and it fits much better in this question than "constantly/continuously". The more accurate translation for "contantly/continuosly" would be "stale".

A little one maybe. „Wciąż” is still in regards of time. As in still meaning now or not yet. „Jeszcze” is more universal. Can't recall at the moment a situation, where you can use „wciąż”, but not „jeszcze”.

It seems to me slightly different, but yes, acceptable. Added.

"Jeszcze", for me, sounds a bit like "OK, some of my doubts are gone but I have new ones", while "Wciąż" more like "Well, some of my doubts are not gone yet". But this is obviously a subjective opinion.

It works already. But I rather don't want to risk people trying to write "moje wątpliwości"... whose else doubts one could have, after all.