I would say #1 makes good sense to me but I personally would not shell out one dime out of pocket for #2 and #3 without more information.
Do you have something going on with your eyes other than dry eye?
By "pictures" of the front & back of the cornea what kind of scan do you mean specifically?
By "higher order aberrations" I'm assuming that's wavefront aberrometry.
What's the stated purpose of #2 and #3, and how will the answers help with treatment decisions?
Osmolarity (#1) is directly connected to dry eye and is increasingly used to test for severity. (What it's used for clinically other than to assess you at regular intervals I don't really know.)
Aberrometry and other scans are not tests frequently done for dry eye in routine clinical practice. Usually related to other vision or disease issues. HOAs for example can help determine the proper course for some vision treatments such as for people who've had a poor outcome from a laser eye surgery. I see wavefront scans mentioned now and then in the dry eye medical literature but other than for research purposes I'm not familiar with a reason to test that in clinic. I'm not saying there isn't a reason, mind you, just that I don't know it.
Personally before paying out of pocket for any testing I would want to know the reason, i.e. what kinds of things they're looking for
The Dry Eye Zone