Yes, if the app supports the different use cases for the Fediverse. Most types of content will work, but not many apps support displaying Lemmy posts next to MobileZon event organisation.
Most apps on the Fediverse use ActivityPub, but there are other protocols like OStatus. You can’t always mix those, if you want to be able to use both ActivityPub and OStatus/diaspora/Zot, you’ll have to pick a server platform that implements all the protocols you want, and an appropriate app for on your device.
For the best results, something Mastodon-like seems to work best. Fedilab seems to have excellent support for all manner of Fediverse implementations. I don’t know if they have an iOS version, but maybe it’ll help if you Google “Fedilab iOS alternative” or whatever.
That said, you can use the plain and simple Mastodon apps (there are a bunch of alternatives that’ll all work with any Mastodon server) to interact with most of the Fediverse as well. The issue is that if you want to interact with services like Lemmy, you can run into rather frustrating usability issues, like your timeline getting spammed with boosts. Lemmy/Kbin work quite different from how most of the Fediverse works and not every app is able to deal with that in a user friendly manner.
Services like Mastodon, Pixelfed, IceShrimp/Firefish/CalcKey/MissKey, WriteFreely, and Pleroma all seem to interoperate with each other perfectly fine. Same with WordPress blogs that have ActivityPub enabled.
Filters aren’t part of any Fediverse spec so it’ll differ per platform and app. Mastodon doesn’t seem to let you import filters, but other apps might. I can’t help you with that, unfortunately.
On the technical side there’s nothing preventing an app from implementing bulk filter imports, other than the frontend developer not having time of interest to implement it. Someone could even write a separate app just to load filters into your account. I just don’t think many people are requesting this.