Literally every single modern chat platform has support for stuff like that, and for a reason. Discord became popular because it combined those modern chat features with the ability for every community to create its own private little "server" - while at the same time making it trivial to participate in multiple "servers" at once.
IRC servers do also support profiles.
I think the real “issue” with IRC is that its users generally prefer the minimal UI. So there isn’t an high enough demand to make prettier UIs. But there are web clients that are a little less basic.
For what it’s worth, I’m in that minimal camp too. I wish I could still connect Slack to IRC.
No, you cannot. You cannot, because you need a team for this, and they need salaries, and unless you push ads into people's throats, there won't be any.
Email really could have been great, but html and bad actors have made it so much worse than it needs to be.