For the spells in the set that allow you to cast cards for free (i.e. ___'s Expertise), the 'free spell' half resolves before the Expertise card hits the 'yard. You can't Archaeomancer/Mnemonic Wall for free off of the Expertise spell, to get the same Expertise spell back. Well, immediately, anyway.
Also of note, the first part of the Expertise card resolves (e.g. Act of Treason for the red one), then you cast the 'free spell' from your hand, then
triggered abilities that triggered if the first part of the Expertise spell had any targets. But if said target becomes illegal (e.g. in response, sac my creature) you don't get the free spell at all. (source
Btw... you can use one of these Expertise cards to cast both halves of a Fuse card (Beck/Call
) for free, yeah?