The Republican Party has the House of Representatives locked up due to gerrymandering until some core constituency departs.
Well mostly no and a little yes on your comment.
No, its not all because of gerrymandering that the R's have a majority in the US House. Its that the R's have a natural advantage in the race for the US House majority. Their voters are more spread out geographically than the Dems votes are. 16 out of the last 20 years the R's have head the US House Majority and 4 of them when the Dem had he US House Majority were because Bush W. was hated in 2006 and he GOP had a bad year electorally in 2008.
Yes, the Dems would have more seats in the US House because of GOP gerrymandering but not enough for a Dem US House Majority if the map was neutral(no gerrymandering.)
This is absolutely true, and why there ought to be multi-member districts. The fact of single member districts helps Republicans right now, but in general it provides a structural advantage in the House to whichever party has its support base more spread out geographically.
Well the "Electoral College Map" helps the Dems right now though too, that's another way of looking at it.
Sure, but that's by happenstance, and state lines are fixed. Generally the action is in swing states, which tend to be states with much less of their population concentrated in urban or rural areas, but more balanced between the two.