I guess I was more concerned about camera shake. I am hoping that since the FF is not cropped, it won't be as sensitive to camera shake.
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not only CAN you use it, you absolutely SHOULD use it with a FF camera. the 85mm f/1.8 USM is an excellent lens, great for portrait and event shooting. I like it on FF far better than I like my 50mm f/1.4 USM for some reason, it's got a little less halation and some more pop to the images at f/1.8 and f/2.
"Do FF cameras perform better in low light conditions such as in a high school gym or at an outdoor stadium at night? "
What do you mean by "perform better" Better IQ, Better sensitivity, faster focusing, faster metering?
There are different answers to these different questions, you need to prioritize the issues so you can get an answer that meets your needs
And then the Autofocusing speed and metering speed come in to play as these, too, will limit your ability to get that special shot
There is no absolute here, you need to prioritize your needs and go from there or you will end up with a combination that fits someone else's needs and not yours