Ydw is used for the the "fi" and Ydyn is used for "nhw"
Ydw i'n mynd i'r siop?=Am I going to the shop?
Ydyn nhw'n mynd i'r siop?=Are they going to the shop?
The question variants would be easier to work out if the course taught the formal instead of the informal.
The infinitive form of the "be"-verb. Like in English and many other languages, the Welsh verb of existence is highly irregular and none of the conjugated forms look anything like the infinitive (bod: rydw/rwyt/mae/rydy/rydych/maen; be: am/are/is/are/are/are).