My suggestions on the various items...
1. Buy a waterproof/water resistant phone. Phones can be expensive, but it is a pretty small portion of the cost of a 14000 mile trip.
2. I have not found glare to be that huge of a problem for a few reasons. First you can actually see the screens of most of the newer phones pretty well. Second you really don't need to be looking at them all that much.
3. I haven't had much problem with this. I never have any features of the phone that I don't need turned on and most of the time it is in airplane mode with the GPS on if I feel I must. On some trips where I can resist tracking progress on the phone and turns are infrequent I power it off most of the time. I never have the "phone" features on. I don't need to get texts or voice calls. Cellular coverage doesn't matter if that feature is turned off most of the time. Otherwise the phone searches for it kills battery and generates heat.
4. See item 3. Get offline maps and make any calls or texts when you do have coverage. Don't promised to call home daily, set expectations low there, then if you do call or text often they will be happy. I find that texts most of the time work better. they go out quickly, work well with a poor signal, and therefore save battery since you get it done and get back in airplane mode or get the phone turned back off quickly. Most of the time you will be on the wide open empty rural road with only a few turns in a given day. Look at the route in the morning and some days that may be the last you need directions.