> 1: Will it work with pretty much any CRT or LCD monitor, or are there specific requirements?
most important: 50 Hz vertical scan rate for PAL
60 Hz vertically (NTSC) and 31.25 kHz horizontally is usually no problem
> 2: Are all Amiga screen modes available via the VGA port?
Yes, but 35 ns pixel modes (Super Hires, Productivity, DblPAL, DblNTSC) will be displayed with resolution halved (every other pixel doubled/missing) due to Amber limitations.
> 3: Are there any quirks/limitations I should be aware of? :-)
see above.

A general (potential) problem is horizontal tearing ('combing') that will be visible with quickly moving objects. This is caused by assembling two fields not generated simultaneously but 20 ms apart. This is a general
deinterlacing problem and very hard to overcome (Amber uses weaving).