Would it be possible to get all Web UI versions (example Horde5 or Horde (old)...) to share their Filters together? Seems that they overwrite modifications that have been done with different Web UI...
No, they're completely different installs and different databases. It's expected a user will choose one or the other.
And... How about plugin for Thunderbird that would allow me to create/modify server side message Filters without going to Web UI? Opening Web UI only because of creating new Filters is frustrating.
Agreed. Sieve is the future, but we're not there yet.