Huh. I'm just browsing Lemmy in a Firefox tab - and the reply dialog sometimes opens right up and other times leaves me wondering if I really hit that button! I wasn't sure if that was another thing where my instance had to "ask" the federation if I could reply before giving me the dialog or something.
As far as I understand it federation shouldn't have anything to do with commenting on your own instance but rather after when it gets sent to other instances.
It uses activity pub, a protocol that allows servers to share content. So when you post on an instance, it became available for other instances to consume your content.
About slowness, it can be that your instance it being rate limited, or it is not powerful enough to process all its users. You can try another instance.
If you're replying to a community on your home server, all actions should be similar levels of responsiveness, I think replying to another servers community may involve "some" active communication with the instance? Simple way to test this, if you are replying a lot on to another servers community, since you are browsing anyway, would be to just open the server/community directly and click around, if it's feels a bit slow, then that server is overloaded by a bit and that's probably the source of your issue. Otherwise we need someone with deeper knowledge in this thread.
Everything you do on your own instance is against a cached version of the original post that is saved on your instance. Your instance sends updates in the background, the other instance can be entirely down and you can still browse, comment, and vote as normal on your own. The updates will just stay local though.