It seems that out of combat, the shield bar regenerates faster than the hull bar, is this true?
Yes, and there are research techs to increase both regeneration rates (as well as amounts). Also, both regenerate in combat as well.
It seems that the hull bar usually doesn't start going down until after shields are fully depleted, is this true? Are there times when I lose hull before shields?
Yes to both. Traditional weapons need to deplete shields first before they start damaging hulls, but some ships have special abilities that bypass shields and eat away at the hull, and Vasari Phase Missiles have a chance to bypass shields and do direct hull damage.
Each ship also has a "shield mitigation" percentage, how does this relate to shield and hull depletion?
I've seen two different ships of the same type with different "shield mitigation" percentages. What affects a ship's shield mitigation value?
The lower the shield hp gets, the more damage it starts to mitigate. At max shields, they mitigate 20% damage (for example, if a weapon does 20 damage and you have 20% mitigation, your shields will take 16 damage), when they get dangerously low, it's common to see 50% or so mitigation. It doesn't relate to hull hp at all beyond buying more time until the hull starts getting damaged.
Hope this helps
And don't worry about which forum
If you want, feel free to hop on the Sins IRC channel (irc.stardock.com #sins, or from SDC). Myself and others usually sit around there and are generally happy to answer questions
