I'm going to specifically answer how to use the probability tree to get win/loss ratios.
For starters, your math becomes very ridiculous to hand-design a flowchart. I didn't even finish the first player attack and got this:
So, let's change your numbers a bit so the drawing gets done today. Now, both player and npc have 15 health, player has a 50% crit chance, npc has a 25% crit chance, both player and npc do 5 damage, and all crits do double damage. Also, they each attack once per turn regardless, and I'll assume the player wins a tie (i.e., both player and enemy would hit 0 health or less on the same round).
This means that each round there are 4 possible outcomes for damage. PHit/EHit, PHit/ECrit, PCrit/ECrit, PCrit/EHit, with probabilities of 50% x 75% = 37.5%, 50% x 25% = 12.5%, 50% x 25% = 12.5%, 50% x 75% = 37.5%.
Now we get this:
In each box, the first number represents the probability of that box occurring if the preceding box happened. Then PxD gives the player's damage, ExD is the enemy's damage, PxH is the player's remaining health, and ExH is the enemy's remaining health. The final percentage is the cumulative chance of getting to that box, calculated by multiplying each conditional chance in the chain (and rounded a bit, so the final totals won't be exactly 100%). Orange text means the player killed the enemy, red text means the enemy killed the player.
For a specific example, let's take the left-most branch each turn. 37.5% of the time, both player and npc roll normal hits, doing 5 damage each, leaving them at 10 health. After that happens, there's a 37.5% chance they each roll normal hits again, doing another 5 damage each, leaving them at 5 health. Finally, there's another 37.5% chance they each roll normal hits a third time, doing a final 5 damage and killing each other. Since we said the player wins a tie, this counts as a win for the player. The total probability of the fight ending this specific way is 37.5% x 37.5% x 37.5% = 5.2734375% ≈ 5.3%.
So the player loses on the second round 11% of the time, wins on the second round 74% of the time, and wins on the third round 14% of the time. Total odds are that the player wins 88% of the time and loses 11% of the time.
Applying to your Numbers
Using your example numbers, you'd need to have a lot more branches, including the fact that many branches include no damage when no attack occurs on that particular round. Which means you'd likely want to automate the process instead of doing it by hand.
I'm not exactly sure how you got your charts, but I think you can convert it to similar numbers by multiplying each of the player percentages by the percentage of player wins, then the same for the enemy chart. So, for example, if the player wins 80% of the time, the first number on the chart becomes 80% x 1.4% = 1.12%. Then the first number on the enemy chart becomes 20% x 3.6% = 0.72%. Etc.
My gut feeling is you can't do what your edit says to get 82%. Each chart sums to 100%, which means each number isn't a percentage of the total, so you can't just add the percentages. You can add the percentages say that 71% of all player wins occur in the first 9 seconds. But you don't know how often the player wins, so you can't say there's a 71% chance the player wins by 9 seconds.
Your chart says there's a 71% chance the player wins by 9 seconds. Then it gets complicated. There's a 29% chance the player doesn't win by 10 seconds. 0.2% of that remaining 29% chance involves the player killing the enemy on the 10th second. But this is 0.2% / 29% ≈ 6.90% chance assuming that we got to 10 seconds. Then we have to break that into four parts. Because we could have neither player nor enemy wins, both win, player wins, enemy wins. There's a 3.6% / 100% = 3.6% chance the enemy wins on this turn, with final results of:
In about 89.7% of the cases, nobody wins, so we go to the next step. In about 3.4% of cases, the enemy wins (so the player loses). In about 6.7% of cases, the player wins. And in about 0.25% of cases, both win (so it's a tie). But the total odds are the 29% chance we even got this far times the individual odds of any specific branch happening. For example, there's a 29% x 0.25% = 0.0725% chance of getting a tie on round 10.
So we repeat the same stuff for the next round. Nobody kills anyone on round 11 (100% chance of nothing, 0% chance of other stuff), so we skip to round 12. There's a 29% chance we made it to 10, then an 89.7% chance we went from 10 to 12, so there's a total of 29% x 89.7% = 26.013% chance we get to round 12 at all. The player chance remaining is 28.8%, and the enemy chance remaining is 96.4%. So the odds the player wins this round, given we got here, are 9.8% / 28.8% ≈ 34.0%. The odds the enemy wins this round, given we got here, are 0.2% / 96.4% ≈ 0.21%. Again, there are four possibilities, just like above. Each block is calculated as tie = (e x p), player wins = (1-e) x (p), enemy wins = (e) x (1-p), and neither wins = (1-e) x (1-p), where e and p are the odds of the enemy and player winning given above, 0.21% and 34.0%.
Then we repeat that for every step of the way. Each round will have four options: tie, player wins, enemy wins, and nothing happens (which leads to the next round). In some cases, there will be a 100% chance nothing happens, so we just skip ahead. The final case will have a 0% chance nothing happens. Add up all the numbers for tie + player wins + enemy wins, and you should get 100%. Add up all the player wins to get total odds of the player winning, etc. Assign tie wherever you want, or treat it separately, your choice.