No, you can't. My explanation below will explain why.
Now, i wanna know, i downloaded cogswap.elf, SWAPMAGIC_DVD_3.6.elf and SwapMagic38ce.elf.
Can i install them like rest of programs (put it on MC, make path from configuratoe, and start them succesfully) and play my backups?
You can't do that. Swapmagic discs (CD or DVD disc) cannot be copied - as the PS2 will check the disc for SCE's code (That labels the disc as being "Authentically licensed by SCE").
So, most simpliest, i ise IMGBurn, create .ISO, burn it on DVD-R or DVD+R, or some even on DVD+R DL.
This code is recorded on a track that's far out of a normal CD/DVD drive's range, and hence cannot be copied.
The ELFs from Swapmagic discs are usually useless on their own, as the media check and type identification by the Mechacon needs to be done first (And it's not done by the ELF). The ELF only stops the drive rotor and tells you that you may swap your discs (The PS2's drive door sensors needs to be blocked first).
You can't, but you can use ESR to do something similar (Check the ESR forums/guide for details).
Is this posible, so, load mcboot, choose one of these 3 programs, insert backupdisc, and start?
SCPH-10000 S. MINOKAMO v1.01 (Defunct)
SCPH-10000 S. KISARAZU v1.00 (faulty)
SCPH-15000 S. KOHDA (With warranty seal!) :D
DESR-5100 S. EMCS