I use WeeChat (https://weechat.org/, running on my server) and Glowing Bear (https://github.com/glowing-bear/glowing-bear) to connect to it from wherever I am (desktop or mobile), it works very nicely. Because it's self-hosted, it has higher setup overhead than signing up to slack, of course. But it does solve IRC's mobile and multi-device problems for me wonderfully. (I'm one of the Glowing Bear developers)
Only if you use plain IRC. If you use something like irccloud, that is prevented. Which can be thought of as a "webwrapper" for IRC. I have been using it for some time now and I enjoy it.