First you can lookup camera compatibility starting with Apple's own fully tested models here:
Lookup Canon and see if your model appears. When I search I found this entry:
|Canon VIXIA HF G10||AVCHD||HDD / Memory||NTSC|
Video stabilization limitations more...
It would appear it is compatible, that it has an internal hard drive or memory card depending on what you want to record to. And if it records to an internal hard drive, then the only way to transfer video recorded to that is via a USB cable as that is the connection the camera comes with. Firewire was used/still used by MiniDV camcorders that record standard def to MiniDV tapes. High Def cams now connect with a USB cable most often.
Re: SDXC card support. You would have to buy a very recent Mac to have an SDXC card slot. You can probably find out if your laptop has it, but if you don't see any SD card slot on your Mac at all it's not going to read an SDXC card without a card reader (which are really cheap, like less than $12 these days). So use your best judgement, and know that your HD footage when it is imported is going to be rather large and take up lots of space on your hard drive. You might also want to buy an external Hard drive when you get the camera so you have room to grow early on.