Will Discourse work on a non-standard port like say :5443 vs :443?
No it will not work.
what if I install the Discourse in development? 3000 is it default port. Will it work on port 3000?
Technically Discourse will run on any port you want it to.
For self installers that follows https://github.com/discourse/discourse/blob/master/docs/INSTALL.md, we don’t provide support for custom ports aside from the defaults that we recommend.