That would work but might be drying and irritating with the ethanol and benzalkonium chloride. Looks inexpensive enough to try. If you have problems, there are some other formulas out there with ethanol and glycerin, and of course ethanol with propylene glycol.
I would personally err on caution and look for something without benzalkonium chloride. You want to deliver the drug to your skin without nuking the natural flora on your scalp and hair.
Probably fine. The numbers I remember are 50-70% alcohol, 5-20% glycerin, 10-30% distilled water. Dissolve fin in alcohol then combine with the rest. Less glycerin for less sticky feel or faster absorption.
Yes I think glycerin is greasier from what I remember. PG is more popular in most topicals. Perhaps consider a test with both and report back on your findings. We’re all making it up as we go