How is combat strength calculated?

Can someone help me figure a few things out, please? I've been stuck on a few battles for days and I cannot work out how to progress. I am extremely new to this game (been playing for maybe 2-3 weeks).

• How is the level of the companion calculated? Is it taking the average or the level of the lowest card? Why does the auto-equip add cards that are much lower than the suggested level of the fight rather than just having less, stronger cards?
• Is it more important to have the level match or the stellactrum match? Is it better to have level 1 cards with matching stellactrum, or go for the level 40 cards and power through?
• How significant are the cores, and should they really be upgraded? The boons for upgrading them seemed pretty small...

I am not really looking forward to sitting down and working out the math, is this recorded anywhere? I can't work out where to get the best bang for my buck.