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.
<em>This afternoon, I have to go there for mom.</em>
2.) Monique est y'allée parce qu’elle n’avait plus de timbres.
<em>Monique went there because she didn't have any more stamps.</em>
3.) Thérèse et moi, nous y'allons pour la boum de Paul.
<em>Thérèse and I are going there for Paul's party.</em>
4.) Maman et Papa y vont ce soir?
<em>Mom and dad are going there tonight?</em>
5.) Est-ce que tu y'as mis des pommes de terre?
<em>Did you put potatoes in there?</em>