Related to #2, there is also zero-width non-joiners (ZWNJ).

I'm in the process of packaging string-width in Debian, and as a low-cost, acceptable solution to all these problems I propose to replace the dependency on is-fullwidth-code-point with wcwidth.js. This patch does the trick:
https://anonscm.debian.org/git/pkg-javascript/node-string-width.git/tree/debian/patches/01-wcwidth.diff

We've created a minimal test suite of strings with zwj and zwnj, you can find it here:
https://anonscm.debian.org/git/pkg-javascript/node-string-width.git/tree/debian/patches/02-test_zwj_zwnj.diff
[sorry we also switched from ava to mocha since ava is not available yet in Debian ...; run them with mocha -u tdd]

As pointed out in #2, the right number of columns required to display an emoji zwj sequence is debatable, so the tests are only there to guarantee we're at least reproducible.