I've got LInux computer with NFS server in kernel mode.

I've installed UNIX services and now can mount NFS share with mount -u:user -p:* server:/home/user/ z:

But I'm always getting read-only access, but now write access. This doesn't depend on user I use (I can use no user but still have read-only access or use root user from my Linux). From Linux machines I'm getting rw access with no problems. What should I check or do to get rw access?

You will only get read/write access to an NFS share on a remote unix box with SFU when the User Name Mapping server component is installed, and the UID for the current user matches the UID of a user on the unix system. I've not tried SFU for the client, but I know on Windows server after installing SFU 3.5 these were required, or the behavior you see is expected.