Your
Day's Undoing ruling was correct. The replacement effect from
Alhammarret's Archive is applied as normal to the cards being drawn from
Day's Undoing, and while
Chasm Skulker's ability also triggers during this process, those pending triggers are wiped out by the process of ending the turn.
As for the interaction between
Alhammarret's Archive and
Monastery Siege, your guess is pretty much correct. The player will draw their normal card for the turn, and then when
Monastery Siege's trigger resolves a few moments later they will draw two cards, then discard one.
Additional Sieges will operate the same way as the first, so with multiple Sieges the player will draw once for the turn, then draw two and discard one for the first Siege, then draw two and discard one for the second Siege, and so on and so forth for however many Sieges the player controls.