To boot Ps1 backups on a ps2/PsTwo/Ps1/PsOne u need a swapdisc like Breaker Pro v1.1 or a ps1 Gameshark disc.
To boot ps2 backups with cheats u can try this (dosnt always work tho'):
1. boot your ps2 Gameshark/Action Replay/CodeBreaker and select the cheats u want.
2. insert swapmagic disc (cd if cd-r backup or dvd if dvd+-r backup) when asked by GS/AR/CB and press key to load swapmagic.
3. swap in your backup (cd-r or dvd+-r)
4. press x ... and it boots with cheats