I'll quote a short passage from Hungarian: an Essential Grammar
The subjunctive is used in questions in the first person singular and plural, to express ‘should I/we . . .?’ or ‘shall I/we . . .?’ In this usage, the coverb is not removed from the verb.Megmondjam nekik az igazat
? - Should I tell them the truth?Táncoljunk?
- Shall we dance?
The subjunctive is also used in indirect questions; the meaning is similar to the previous usage, expressing ‘should/shall one . . .?’Megkérdezték, hogy felírják-e az új szavakat
. - They asked whether they should write down the new words.
In subordinate clauses:
1. If the desire or will of the subject of the main clause is pressed upon the subject of the subordinate clause, the subordinate clause will contain the subjunctive verb. The verb in the main clause may be one of will: akar
‘request’, ‘ask’, javasol
‘recommend’; or it may be any verb of communication through which a wish is conveyed: mond
‘send the message’, etc.Azt írták, hogy jöjjek haza
. - They wrote me that I should come home.
2. The subjunctive is used to express ‘in order to’ or ‘so that’; this is often combined with a main clause introduced by azért ‘for that reason’.Sokkal többet kell gyakorolnom, hogy igazán jól tudjak zongorázni.
- I have to practice much more in order to play the piano really well.Arra törekszik, hogy új állást kapjon
. - He’s trying to get a new job.
3. Subordinate clauses following impersonal main clauses are also in the subjunctive.Szükséges, hogy előre telefonáljak?
- Is it necessary that I call in advance?
4. The subjunctive is used in subordinate clauses where the main clause expresses a lack, absence or inability (to fulfill a goal).Nincs kivel kártyázzak.
- I have nobody to play cards with.
In your case:Menjünk
! - Let's go! Shall we go?De jöjjön Ági is
! - Let Ági also come (I insist that Ági come too)Én is menjek
? - Should I also come?
If you have more questions, feel free to ask!