Can I set up the camera app so that I can take photos by tapping anywhere on the screen instead of on the camera icon while it's on? I used to be able to do it with my 925 but I can't with the 950.
You might be able to do that previously but in latest Windows Camera app, tapping anywhere on the screen instead of on the camera icon results in manual focus. This helps you out to focus anywhere you want. Since you are 950 user, I am dead sure that you are quite updated and hence you can use manual-focusing feature instead of tapping-anywhere capture. If you still want to capture by tapping anywhere please consider Office Lens app. It is much better and handy. If you still want that feature back then I am sorry it is not possible.
It seems this is not possible in the current version of the camera app on Windows 10 Mobile. You should add this suggestion in the feedback app. Meanwhile there are some thrid-party camera apps in the store that might provide you that functionality.