Neither Jack nor Paul has got a computer. — Ни у Джека, ни у Пола нет компьютера.
We have done everything. — Мы все сделали.
Neither Jack nor Paul — the third person singular. We can't use have. We use has for the third person singular.
The second sentence is in Present Perfect. Present Perfect is formed with the help of the auxiliary verb have / has (third person singular) and we use the third form of verb. Negative — have / has + not + verb.
We have not done everything.
Interrogative — Have / has + subject + verb.
Have we done everything?