Question: What type of doubts invalidates wudu' and what type of doubts does not invalidate it according to the madhhabs of the Hanafi and Maliki? If a person who doubts whether or not his wudu' was nullified or who has forgotten the fact that he has wudu' remembers later that he is on wudu', is his wudu' considered to have been nullified because of the doubt he initially had?
If he remembers later that his wudu' was not nullified, his wudu' remains valid according to the Maliki Madhhab, too. According to the Hanafi Madhhab, if he is certain that his wudu' was nullified and doubts whether or not he renewed his wudu' afterward, he is obligated to make a fresh wudu'.
According to the Maliki Madhhab, if he does not remember whether or not he made wudu', he is considered to be without wudu'. But if he remembers later that he made wudu', he is considered to be on wudu'. That is, forgetting the fact that he is on wudu' does not break his wudu'. According to the Maliki Madhhab, if he is not sure whether he broke his wudu' or not and has doubts about it, he is obligated to make a fresh wudu'.
Question: When I make wudu', is it a condition that the fact that I am in a state of wudu' should constantly be present in my mind? I forget about my wudu' when I am engaged in an activity. Is my wudu' nullified when I forget about it?
No, forgetting about your wudu' does not cause it to be nullified'. In fact, it is impossible for it to be constantly present in the mind.
If one is certain that one made wudu' but doubts whether it was invalidated or not, one is considered to be on wudu'. However, if one is certain that one broke one's wudu' but doubts whether or not one renewed it, one is obligated to make a fresh wudu.
Question: Supposing a person is sure that he made wudu'. After hours pass, he says that he has forgotten about his wudu'. Is such a person considered to be on wudu' according to the madhhabs of the Hanafi and Maliki?
Forgetting the fact that one has wudu' does not break one's wudu' in either of the two madhhabs. That is, if such a person is sure that he made wudu' and has not broken it, his forgetting the fact that he is on wudu' does not harm his wudu' in either of the two madhhabs.