On my current D3100, I can only take a picture when the camera is focused, something that I've got used to and find it great. Would I be able to activate/deactivate this on the D7500?
This is known as AF-S mode, where the camera will only take a shot after it's confirmed to have a focus lock. On the D7500, this is controlled via the second dial below the mode selector on the top left. It's easy to miss if you didn't know it was there. This dial is where you select AF-S, or AF-C (continuous), the quiet modes, mirror up, and the timer.
My camera lives in AF-C, since I tend to be more in action and use back button focus. And then I always spend 10 minutes looking in the menus for turning on the timer - I forget that this is where it lives!
Careful. It's the COMBINATION of mode and priority selection (a1, a2) that delivers what you want. When you select AF-S, priority selection defaults to FOCUS - i.e., the camera won't release the shutter until focus is confirmed on the half-press.
But you can use setting a1 to change priority selection to RELEASE, and even if focus isn't confirmed, the shutter will release. a2 works the same way for AF-C mode.
Now it may not seem to make a lot of sense to have an a1 setting - AF-S is supposedly for deliberative shooting situations in which the camera doesn't move relative to the subject, so focus should always be confirmed on the half press - but it's there.
The a2 setting makes a lot more sense to have - the default setting of RELEASE makes sense for BBF operation, but some folks like myself find that you can get better focused shots in portraiture and such if you both continuously focus until shutter press (AF-C) and confirm focus after shutter press (a2=FOCUS). This gets rid of the inevitable subject-camera wobble that can throw off close-focused scenes. Of course you have to remember to switch OUT of a2=FOCUS when shooting action, and this is where BBF comes in as a possible benefit.
In the pro/semi-pro level Nikon DSLR bodies, there are multiple options for priority selection - you can have focus on first in a burst with following frames being release priority, etc.. All of these have found some utility in shooting moving subjects.