Ship integrity is your "max health" number. The "health" of your ship itself is your hull, which as you can see is grayed out because your hull is repaired to it's maximum value. 0% integrity is a misnomer, it means that the integrity of your ship internally speaking can't drop any lower; your "maximum health" can't go down any more, but you still have "health."
The repair cost for your integrity is based directly on the value of the ship when you bought it. Your rebuy cost is based on the value of your ship and everything it's got equipped. You should repair the integrity time to time and not just ignore it, thinking "repair all" will fix that. You need to manually do it every once in a while. Also, you're going to blow up your ship over a thousand credit difference? Okay...