Now I really have broken the build

Okay, I've got two patches ready to fix my two problems. Do I simply make another commit and push it?

Yes, push whatever is needed to fix the build if the fix is fairly simple (else revert and get an LGTM with the fix).

Next time I’d recommend creating and pushing a revert first if you can’t quickly figure out the issue.

Can you explain how to revert for someone who is a 2 on a git scale of 0 to 10?

$ git revert $COMMIT
creates a revert of the commit
https://git-scm.com/docs/git-revert for more info

From that page:

"Given one or more existing commits, revert the changes that the related patches introduce, and record some new commits that record them."

After my copyediting instincts calmed down, I found another description and I understand what it does. Thanks!