Is it permissible for a husband to look at his wife's 'awrah and derive pleasure from it, and what is the wisdom behind permitting this while prohibiting looking at the 'awrah of other women, and is it permissible to use the hand in the marital relationship to aid ejaculation inside the wife's vagina?

A man is permitted to look at his wife's awrah for pleasure. This is permissible and poses no risk of corruption, unlike looking at the awrah of non-mahram (definition) women, which leads to temptation and is unlawful.

As for stimulating the wife's private parts with the hand, there is no harm in it. However, using the hand on something other than the wife's body to arouse desire for ejaculation is forbidden masturbation.

These questions indicate yielding to intrusive thoughts that lead to doubts. The remedy for this is to busy oneself with acts of obedience and seeking knowledge, and worship, such as prayer and fasting, and to avoid innovations. They also indicate a type of waswasa (obsessive whispering), so one must constantly make supplication and show humility, disregard the waswasa, and perhaps consult a psychiatrist.