Hi beaddict, my thoughts on your questions.
1. Yes, you can partially foil. I suggest Googling this/You Tube it, as some foiling systems only work on toner, there are others that work on inkjet. You'd probably have to print the part you want to foil first, do the foiling, then go back and print the rest. So this will probably be the most time consuming part.
2. The Gemini foiling system is quite new, but as I recall they have a lot of dies for doing Wedding invites. Link
HERE for their USA site, you can see the machine/dies etc.
3. Yes, probably, lol.
Filigree dies do come in all sorts of shapes and sizes, have a look for Sue Wilson dies, she does a huge number.
To be honest, the Cameo should do the filigree die cutting with ease, the advantage being you are not stuck to a certain size, you can resize your shape to be a perfect fit for your invites. I'd definitely suggest doing a trial run, maybe cut out a few different designs for her to choose from?
Just remember to allow yourself at least double the time you think they'll take to make, it's surprising how long it can take to get them done, and you don't want to find yourself stressing over a deadline. Good luck. X