Hello!
In general, the component works fine.
But when I trying to save category settings or Global K2 setting component freezes in 1 or 2 minutes.
Then page displays error 504 Gateway Time-out.

I have same issue on different servers.

Hello,
You need to ask your hosting provider (or look at your logs) which request causes the 504 error.
It is most likely a server related configuration issue.

Krikor wrote: Hello,
You need to ask your hosting provider (or look at your logs) which request causes the 504 error.
It is most likely a server related configuration issue.

I use dozens of Joomla components and this problem only with K2...

A 504 timeout is a generic one, it could be attributed to a dozen causes (eg: memory limits), your hosting provider can pinpoint the issue.