Sometimes it is striking how well-meaning and clear-headed individuals can read the same sentence and come to radically different conclusions.
Starting at 6th level, you can attack twice, instead of once, whenever you take the Attack action on your turn. Moreover, you can cast one of your cantrips in place of one of those attacks.
The second sentence means one of two things:
1. Moreover you
may cast one of your cantrips in place of one of those attacks. [i.e. giving permission for something normally not possible, if you choose, assuming other parameters are met]
2. Moreover
you now have the ability to cast
any one of your cantrips in place of one of those attacks. [i.e. removing the normal spell-or-attack choice and additionally allowing in some circumstances a reduced casting time]
To me, the plain meaning of the text is the former not the latter. You can cast a one-action cantrip as part of the attack action.
Can you cast a bonus-action cantrip? Yes, but I can see the case for no. In any case, you can also cast it with your bonus action, so unless you are using it for something else (which you might be), there's no benefit (and if you do use your bonus action to cast it, you can attack with magic stone or a shilleleagh as part of this anyways.)
Can you cast a cantrip that takes 1 minute? I would say no. I see the sentence as giving permission to substitute a spell, not changing the nature of the spell itself.