As you showed they have some sort of active response to a trauma, in a form of emission of stem cells. This could mean that their normal food requirement is not that much bigger than a human would have.
About their stem cells emissions, it could be calculated from biomass that is required for the healing process. All of the damaged tissues will likely get dissolved by the body, and new ones are built in place. In animals growing 1kg of biomass takes about 10kg of food. Anywhere from 2 to 25.
Another case to consider is pregnancy. When body is making a baby, we can just look at it from the prespective of making a new biomass from food. Total additional food intake is about 24 000 calories, and newborn weight is about 3.3kg, placenta weight 0.6kg, additional uterus weight 1kg. Thats at least 4.9kg of biomass carefully created for a task, using only 8.3kg of beef as a food source. Hmmm... I expected it to be much more. Probably something is off with the additional food intake calculation.
But you get the idea. To calculate how much of biomass is transformed, and use a coefficient of 2...25 to get amount of food required.
If your alien is hit with a bullet, that makes a kilogram of flesh non-functional, your alien would need to eat 2...25 kg of food, at least. Depending how careful the healing process is adapted to be low usage. Thats assuming no blood loss, no infection. Blood loss can be calculated the same way, 1kg of blood (100kcal) is not that far of 1kg of meat (290kcal). Infection can do massive damage to the body and require tens of kg of food. Thin cuts, if wound is closed while healing, can be cheap to fix, not a lot of biomass is required within a thin cut.
Blood loss is likely to be the main danger, in case of a trauma. It can be somewhat fixed with slightly different circulation system. In particular well developed bypass blood vessels, like some humans do. Another benefit is muscles that can contract and stop the blood flow in certain vessels, like lizards do. Then unless this alien is chopped into small pieces, it will be fine, if it has food.
Open wound is prone to infections. So much so that it makes sense to add about equal amout of white blood cells to the stem cells, to always patrol the damaged area, to quickly form pus, before more tissue is damaged by the microbes. Considering the scale and time requirements you cant allow the wound to dry, that is an easy way to reduce bacterial load. So your aliens' wounds will be constantly wet and will constantly drip pus while they heal. Extremely wasteful in terms of energy, but if your aliens can afford to eat that often, and can digest this much food, its okay. Pus, partially made of white blood cells, would weigh about as much as the damaged flesh. And is as expensive to make.
All together, blood loss, pus and the formation of new tissue, consider the cost to about triple, from 2...25 to 6...75 kg of food per kg of damaged tissue. For the case of open wound, wet wound, non sterile healing process.
Keep in mind, that even if food is present, ability to digest the food is limited. Humans cant eat more than about 3kg of beef equivalent of calories per day, simply because the digestion system isnt powerful enough.
Alltogether, assuming 30kg of food for 1kg of damaged tissue, a medium sized gunshot wound, and human-like digestion system, it will still take 10 days to heal it, simply because of food intake limitation.
Even faster healing rate would really push the limit of getting rid of the heat, using special food only because normal food cant be digested fast enough, not even cooked food.
All of this assumes limitless amount of water available... In nature water is often a limiting factor for such extreme level of activity.