"Do I go to him?"
Translation:An dtéim chuige?
an in this case is the question particle - it signifies the sentence as a question. It's dt because an here triggers eclipses
Yes. Shall implies that your asking permission, and that's not covered by this sentence.
linguists can call An+eclipsed verb the interrogative, ie the question conjugation
Linguists call this an an interrogative particle.
Particles occur before the verb which is otherwise at the start of a sentence, and change the way that sentence is interpreted. An interrogative particle turns a statement into a question, a negative particle negates a statement.
Téim chuige - "I go to him".
An dtéim chuige - "Do I go to him?".
Ni théim chuige - "I don't go to him."