Currently EventSub only supports the webhook transport medium, which requires you to host a publicly accessibly HTTPS server that Twitch can send the events to.
A websocket transport method is currently in development, which would allow you to make an outbound connection rather than needing to host a server, but this is not yet available.
There will also be more transport methods in the future which may or may not require hosting a server, but none other than the previously mentioned websockets have been announced.
Poll the applicable endpoints once a minute. For example, if you want to know of new followers you use the Get Users Follows endpoint, cache the results, then in a minute make another request and look for changes to see if there have been new followers. Many other things like subs can be tracked in a similar way.
Bits usage, such as Cheers, can be tracked by your connection to chat, as you mention already using tmi.js so you can use that library to listen for when Cheers happen.