Can a customer use their own modem for fixed Fibre broadband?
You can but you won't get any support unless if you're using their provided router.
And their provided router these days (the same router Spark are using) is actually very good and is even better than most consumer grade off the shelf routers.
Seriously, if you're wanting to use your own router the consider another ISP (Voyager is very good).
Stick with your current ISP. Also there is no reason your IP Camera shouldn't work...
You'll still need to either purchase yet another smart modem or sign up to a 12mo contract for Skinny.