Claim doesnt allow to use world block importer, as in this basic system should work, but doesnt in claim

Pretty sure, if I recall correctly, the player simulator also doesn't work without completely disabling chunk protection. Probably the same root cause given the nature of the interaction.

redstone emitters etc also doesnt work.

If it's a fake player, then I'm afraid you can't fix this through the configs. I'd have to manually add support for this mod.
You can change what options are player-configurable in the main server config file while the server isn't running.

then it would be great if you could add compatibility for that mod, its pretty popular as well

Please let me know if anything else from that mod doesn't work.

It's just the block being protected from being broken. Try turning off mob griefing protection for the claim, if the server has that option configured to be accessible.
I probably should rename the option though.

is there a way to only enable this fake player named [IntegratedTunnels]

also I am the owner of the server yet I cant modify my claim options, how can I enable them

Not sure, but I think I'll have something for it in the next update.

any idea when that would be fixed, I am having some issues because of that.