Yes with a sincere repentance I think it’s only 3 days if it’s the same. Just don’t promise Allah something you can’t keep from now on. Allah is most forgiving most merciful never lose hope. Allah knows best.
Yes, it is permissible for you to leave fast, however, based on modern technology, you would be driving in a car, so that would not make you tiresome, however, if you are taking a long walk, then it would make it permissible for you to leave your fast. As such, a person on a journey is given the concession that he or she does not need to fast in Ramadan, but ...
If your friend is doing research on the deep web to see how it is being used for the purposes of social policy, then this is obviously not haram but halal.
However, if your friend is using the deep web in order to access things which, given what you say, is haram - say drugs, porn or stolen goods - then this is as haram as it would be in real life.