doubt

Assalamu’alaikum warahmatullahiwabaraktuh. What’s the ruling on doubting the basic principles of Islam? Is he/she considered as disbeliever? From what I know doubt is not denial. I may doubt for the Day of Resurrection for some minutes, but after searching and finding proofs in Qur’an and hadeeth, I won’t have anymore doubt about it. Does that render me as a disbeliever; although I never denied the fact that the Day of Resurrection will come? Thank you.

As-Salamu `alaykum. Very often when I stand up to pray, I have doubts in my mind as to whether my purification or wudu' has been nullified or not. What should I do in such a situation: Should I leave the salah and purify myself and then resume my salah, or should I simply continue my salah and not bother about such doubts?

As-Salamu `Alaykum. If a person has doubts in his Salah, i.e. not sure whether he has prayed three Rak`ahs or four, what should he do?