Hi!
I use my router (rb951g-2hnd) in home network. Sometimes power outage may occur, router connected without ups. After power restore router boots up ok, in log I see "router was rebooted without proper shutdown".
My questions are:
1. this log message is information only or more critical and someday power fail may brick router OS?
2. Do I always need to shutdown router from (for example) winbox before turn it off from AC outlet (cut power)?

1. this log message is information only or more critical and someday power fail may brick router OS?

Only information for you

2. Do I always need to shutdown router from (for example) winbox before turn it off from AC outlet (cut power)?

No, newer

On mikrotik wiki found article about Ups support. http://wiki.mikrotik.com/wiki/Manual:System/UPS There is some information:
"This feature enables the network administrator to monitor the UPS and set the router to ‘gracefully’ handle any power outage with no corruption or damage to the router."

So again, does router maybe damaged or be corrupted by power outage?

I can assure you it will, if it suffers several blackouts per day NAND will get corrupted in months.

Can attest to it . You are better off shutting down the routerboard down properly and disconnecting it.Netinstalling from scratch most of the times brings from back from the dead , but I have 3 sitting in a box that are essentially zombies.If you want to continue running , you are better off buying a UPS w/ battery pack or inverter to keep on going.

Sooner or later you will have a dead routerboard on your hands.

Source : 5 Dead RB750's from satellite offices due to bad power issues.

You are overthinking it. Power outages occur, it is inevitable. If uninterruped service is the thing you need then sure go for ups. But a power outage will not damage the router. A power surge could damage it like any other electrical appliance, but not every ups will guard you from that either.
I have devices running for many years, a lot of power outages, no problems. The messase is informational so when a board is restarted you can see the log and know what caused it to reboot.

The point here is ocassional power outages may not damage the router. Several power outages per day, will.

Had some config resets after power loss on 951G and mAP 2n... so I'm preferring to shut down the router properly.

Each forced shutdown (due to a power outage or yanking out a power cord) introduces chances for the router's file system to be currupted. Thus, graceful shutdowns should be performed whenever possible.