I\'m relatively new to Mercurial and my team is trying it out right now as a replacement for Subversion.
How can I commit and push a single file out to another rep
Since you said easiest, I often use hg commit -i (--interactive) even when committing whole files. With --interactive you can just select the file(s) you want rather than typing their entire path(s) on the command line. As an added bonus you can even selectively include/exclude chunks within the files.
And then just hg push to push that newly created commit.
I put more details on using hg commit --interactive in this answer: https://stackoverflow.com/a/47931672/255961