Welcome to the community! 
Just a note, that generally itâs best to break this kind of thing up into a few more targeted topics, as kitchen-sink topics are hard for folks to respond to, and will typically end up twisting in the wind a bit.
Also, thereâs a great number of resources on most of your questions here on meta.discourse.org. A good way to familiarize yourself with the community is to spend a bit of time reading topics on subjects youâre interested in.
Then when you seek further help on a topic, you can ask more targeted questions, and youâll get much better answers. Other folks in the community will appreciate that you took the time to read through the various topics, and will want to help you even more.
Gsuite and Mailgun do different things and you will need both. Mailgun is what you call a âtransactionalâ email provider. Have read up on existing resources here and elsewhere on this one.
Yes, digitalocean.com is a great option for self-hosting, and there arenât any issues with using it.
It depends on what kind of chat youâre talking about Have a search for âchatâ here on meta to see what folks have discussed in the past, then follow up in those topics.
The out-of-the-box way to do this currently is to add tags using the WP Discourse pluginâs publishing options. If youâre interested in more than this, follow up in the topic below, or perhaps this one.
Youâll need to write plugin(s) for Discourse and / or Wordpress to do this. Given that youâre interested in coding this yourself, I would point you in a few places to get started: