Replying to Need boots to get your bindings mounted?

I've bought my skis and bindings but haven't been fitted yet for boots, so I haven't bought any. And my local ski shop's boots are ridiculous amount of money for a decent pair so I was just going to get my size and then buy discounted online and save some money. So can they just mount the bindings based off my foot measurement or do they need the exact boot to ensure a perfect set up? Also I read brand new skis should be de-tuned before you take them on the hill; is that true?