Learn Hardcore Latin: Mater rogat utrum tonsor etiam barbam avi cras curaturus sit. - Mother asks whether the barber is also going to tend grandfather’s beard tomorrow.

Mater rogat = Mother asks
utrum tonsor etiam barbam avi cras curaturus sit = whether the barber is also going to take care of grandfather’s beard tomorrow

So:

Mater is the subject of rogat
tonsor is the subject of curaturus sit
barbam is the object of that second verb phrase

Latin often makes this clearer by case endings rather than strict word order.

Why is utrum used here?

Utrum introduces an indirect yes/no question. In English, the natural translation is whether.

So:

Mater rogat utrum... = Mother asks whether...

You will often see utrum when Latin is reporting a question rather than asking it directly. If there were two explicit alternatives, Latin could say utrum ... an ... = whether ... or ....

Why is sit used instead of est?

Because this is an indirect question, and in Latin indirect questions normally take the subjunctive.

So although English just says is or will be, Latin uses: