1. PC HP is normal but you
must roll. No option to take the average. Level 1 is your roll or half of maximum, whichever is greater. You add CON bonus up to level 7 or 9 maybe, but after that it is only the HD roll.
2. MAX ability is 18. 19 for races which receive a bonus (a mountain dwarf could have STR 19 and CON 19 for example). We do this currently with a feat called "Raising the Bar" which allows one score to be 20.
3. I like the idea of a level of exhaustion, but only a failed death save, and don't make 3 death, make it when the exhaustion level equals death (at 6). You could even combine them, so if you already had a level of exhaustion, and then went to 0 hp, a failed death save would put you at two levels, etc.
Three successes would still stabilize, a 1 would be two levels, and a 20 would remove a level as well as stabilize with 1 hp.
Have the death save be modified by CON. It is not a check or a save, so no features or such would further modify it. IMO a person with a CON 7 is much less likely to survive and stabilize than one with a CON 17.
4. Short Rest recovered HP = level + CON bonus. Long Rest = Short rest x2. This way a "fulll day of rest", i.e. 2 short rests and one long rest would be a short rest x4 effectively. That might be too much, though.
Exhaustion takes one day per level you currently have. So, if you have 5 levels (the max since at 6 you die), it takes 5 days to recover, then 4, then 3, 2, and 1. Thus to completely remove 5 levels would take 15 days. If that isn't long enough, you could double it.
5. Sure. Every 4 levels you gain a feat as well as a proficiency to spend on whatever you want (skill, armor, language, tool, etc.)
6. Oy! That hurts, but with the right archetypes and a bit of leniency I would survive it.
