in the phrase 'nous avons acheté' is the 's' sound in 'avons' pronounced? Or is the 's' sound in 'avons' silent? I tried using Google Translate pronunciation but I couldn't quite make the sound difference.
No native speaker. I think that the first "liaison" (i.e. between nous and avons) is obligatory.
The sound z is produced: nuz‿avɔ̃.
The second "liaison" (i.e. between avons et acheté) belongs to the so-called facultative "liaisons". Some natives will make the "liaison", that is, they will produce the sound z as: nuz‿avɔ̃z‿aʃte but I tend to believe most of them will not make this "liaison", at least in colloquial French.
See the recent question:
Do you pronounce the t in ''et un/une'' ?
and the references therein.
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4For me, native speaker, the two « liaisons » must be made. The only difference I see is that in « nous avons », there will never be a delay between the two words, and between « avons acheté », it could be a little delay. After the delay, the « liaison » can be (should be?) omitted. In conclusion nous avons without liaison will be weird for a native speaker, but avons acheté will sound OK with or without liaison. – FredericP Jun 1 '20 at 12:57
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en.m.wikipedia.org/wiki/Liaison_(French) does not list the second liaison as obligatory. – Alan Evangelista Jun 3 '20 at 8:35