Learn English – for vs in in a preposition after the verb “travel”

Consider these possibilities:

I am stuck on the database problem.

This means you can't continue because you can't figure out how to solve the database problem.

You could also say

I am stuck at the database problem.

This means much the same thing, with the nuance that you are stuck at the point of the database problem among a set of tasks you are trying to address serially. You probably can't do anything else till you solve that one. If you use on it might suggest you could do other parts of the task while waiting for enlightenment on the database issue. But on and at are pretty much interchangeable here. I would expect to hear on more frequently.

I got stuck with the database problem.

This means someone left you or assigned you the database problem to solve (with overtones of it being an unpleasant or difficult task).

Yes, the correct preposition is to.

Often these questions can be answered with the help of a collocation dictionary, e.g. this one.

I should say that there are other problems with your sentences. In the first one, you don't say *who learns English but who is learning English. Also, you don't recommend (to someone) about something, but instead you recommend something: I would like to recommend to him a better dictionary (or I would like to recommend a better dictionary to him); also possible are I would like to recommend him to use a better dictionary and I would like to recommend a better dictionary for him to use.