Yes, lots of districts per state, 435 in total who vote, plus 6 non-voting reps from DC, Puerto Rico, etc. I don't think they cross state lines, as it's the state who draws the maps.
Many of them gerrymandered into tortuous shapes - here's one in Maryland a few years ago:
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I've heard it said that the general intention of gerrymandering is to give your side a number where you have maybe 60-65% chance and the other side a smaller number where they have 85-90% chance - don't know if it's true, and I assume it varies by state.