I used to frequent the online Fall forum - they used to have an old school forum but a couple years ago, they upgraded/moved to Tapatalk hosting. In doing some very light googling, It appears they do free forum hosting and have a free mobile app. In using it for the Fall forum, they do have notifications when others reply to you or threads you've engaged in - they have more custom configuration settings, etc. They do support it with ads, but I've never noticed because I use an ad blocker. Here's what that site looks like if you're curious.
https://www.tapatalk.com/groups/thefall/
I can't speak extensively about the app - I did download it and it does work well - being a dedicated app, you don't have to worry about browser compatibilities - it works and it looks clean.