> group messages go into some archive-window (instead of showing up in the chat window like in every over program), sometimes the archive misses them...
Not sure what that even means. Worth reporting.
> pictures are a link to the server, so I have to manually download them all.
I think you need to install the image preview plugin.
For gajim make sure it's a recent version.
Dino-im https://dino.im/ is decent.
poezio https://poez.io/en/ if you want a text client.
converse.js https://conversejs.org/ for a web client.
Public server wise I don't have any recommendations (but i'm sure others have plenty) other than movim. https://movim.eu/#try they have a baked in client (and do a whole bunch of other stuff like micro blogging) but once you have a account, there is no reason you can't use any client you want.
Encryption with omemo is a issue and usability could be improved (I believe people are working on that).