If you're not aiming for number, engagement, reach etc. several seconds or minutes of delay basically make no difference.
Yes, you can't use the DMs here as a general chant (though doing that with the other social networks also always felt weird to me, I mean there's signal, use tools for what they're good at 🙂).

I guess that comes to the result that interactions would on average feel like they're a tad bit slower than on a centralized platform. It depends on your worldview if that's a bad or a good thing, but it goes well with the ethos of avoiding bad faith discussions which are often well correlated with fast paced replies.
Don't get me wrong, it's not a "feature", it's a limitations, but it's not really a terribly serious one as it might look like at first glance.

So again, the best way to see the most up to date state of a profile is to go and see it on their home instance (usually easiest to do through a browser).
Things like replies, DMs and other interactions can also sometimes take a bit more time to propagate when happening cross-instance. Again it would depend on how well provisioned the included instances are for the current load they're under.