Vermintide 2 Chests info.

1) How does power level work regarding chests?
All chests have a power level cap. This cap is 100 for Recruit, 200 for Vet, 300 for champ and Commendation chests. The power level of the items you receive from the chests are dependant on the power of the items you already have to a greater extent, and the level of the character that opened the chest to a lesser extent. This means that once you have hit power level 100 for each item equipped on any given character, that character will never pull a power level 50 item from a chest again. There is some margin for error here, sometimes you will receive an item with slightly lower power than the items you already own, but for the most part your power will continue to grow with each new piece of gear obtained, until you hit the hard cap for that chests power level of course.

2) When should I open my commendation chests?
There is no objectively correct answer to this question. Opening the chests as you get them increases your power level the same way opening other chest would, so it can steadily increase your gearscore. However commendation chests have a power cap of 300 so you can feasibly save all the chests for when you're already at power level 300 for a mountain of maximum level gear. Or you can save the chests for when your items are powerlevel 250+ in order to help jump up closer to 300. Use them however you would like to use them. Each strategy has its own pros and cons.

3) Are there any other ways to increase my power level?
Yes, crafting. Use scrap from older, garbage gear to create new, more powerful gear. Crafting has no cap except the hard cap on all gear. Meaning that, for instance, if you only ever play recruit, and you have several pieces of powerlevel 100 gear, you can craft in order to receive powerlevel 101-110 power level gear, and so forth. Crafting can also turn your whites into greens, into blues, into oranges, and change the legendary effects of oranges and the properties of greens and blues. This requires dust from scraping related color tier items.