I want to check non-root filesystem after each boot. But I want do do it via fstab parameters and tune2fs. Of course first I need to

But I want FSCK to be done with -y option, that is automatically fix any problem. Is it possible?

The periodic check options are ignored by default these days - the filesystem will be automatically checked at every mount by current e2fsprogs. This is not well (badly) documented in the manpages.
How boot-time mounts are handled is a funtion of your init system. Which is of course distro dependent - and systemd changed that significantly too.

You could write a script to do it, and run it each boot.

Of course, it is possible to write such script. But my system is Raspberry Pi 3B with Jessie system. I use it as unit to collect data from measuring sensors to MySQL DB. All temporary file, including MySQL tmp files are moved from SD card to ramdisk. It works 365/24. All data are collected on SSD USB attached disk. So reboots accrues very rarely. The problem is that hardware watchdog from particular sensor, restarts RPi after 5 sec of inactivity. No way to change this time. So I want to FSCK attached USB disk during boot.
One more question. Is it better to use -p or -y option for FSCK, to make FSCK process fully non-interactive, fully automatic.

You should use both p and y for noninteractive repair. And I don't see what the rest of your post has to do with making a script. Just run it a cron job each reboot. Or, make it a service that runs on boot.

As I wrote, its because of hardware watchdog. It simply turn off/on power without shutdown system. I try to write script but the timeout of watchdog if to short to execute it from rc.local of /etc/init.d. It must be done during filesystem mount from fstab. Watchdog activates itself when this one particular process is finished. It is piece of hardware (based on ATTiny) and it interprets several communicates from TTY console. No way to modify it in way necessary for me.

OK, I understand now. I don't think it will work from fstab anymore.