How should I deal with the whispers of the devil with regard to ablution and purity?

Whispers in ablution are from the devil, and so you should take refuge in Allah from the devil`s evil suggestions that aim to distort the religion. Thus, once an organ is completely pure, don`t question its purity since having whispers doesn`t mean that the purity is invalid as it has already been established.

Is wearing a cap permissible for boys, or girls?

All Perfect Praise is due to Allah, The Lord of The Worlds.

In principle, anything is permissible sol long as there is no Sharia evidence prohibiting it, thus wearing the cap by boys is permissible as long as it isn`t done in imitation of the disbelievers. Moreover, a Muslim woman should avoid all that which attracts the attention of men because whatever leads to the forbidden is forbidden. And Allah Knows Best.

I work in a government institution that gives an additional three dinars per hour I work. The manager combines students into a single session because attendance is low, and the material taught to all groups is the same. I am paid for two hours, although I actually taught only one session, noting that my transportation costs one and a half dinars. What is the ruling?

The only amount you are permitted to take/have is for one hour work. And Allah Knows Best.

Is Iddah (waiting period) incumbent on an old woman whose husband had died?

Upon the death of the husband, Iddah is incumbent on the wife regardless of their age. And Allah Knows Best.