0.20.2 backports 1
First round of backports. Covers everything up to and including https://github.com/pandas-dev/pandas/pull/16526

@jorisvandenbossche I can't remember, did you make PRs for batches of backports or commit directly to the maintenance branch? I think I prefer PRs, if only for another historical record.

And I think we want to rebase and merge onto 0.20.x, not squash.