Y refers to a past-referenced place. So, you just replace the referenced locations/places in the sentences with y! You do have to re-order some of the words.
Rewritten Phrases:
1.) Cet après-midi, je dois y'aller pour maman.
This afternoon, I have to go there for mom.
2.) Monique est y'allée parce qu’elle n’avait plus de timbres.
Monique went there because she didn't have any more stamps.
3.) Thérèse et moi, nous y'allons pour la boum de Paul.
Thérèse and I are going there for Paul's party.
4.) Maman et Papa y vont ce soir?
Mom and dad are going there tonight?
5.) Est-ce que tu y'as mis des pommes de terre?
Did you put potatoes in there?