1) I want to perform disk/partition backup of my entire system (i.e. all partitions) and then make a schedule for daily incremental backups. After 30 days I'd like the cycle to be repeated (i.e. full image/backup of entire system followed by 29 incremental backups) but also want the new full backup to replace the old one and get rid of all old incremental backups to preserve disk space. Can Comodo Backup do this?
Yes, if you create an incremental backup job with macro option (in backup step 3). Use the revision number macro with reset after 30 runs. When the revision number goes back to zero, all previous backups are deleted.
2) Can Comodo Backup perform system recovery in case something happens to the hard disk? I noticed that the WinPE disk described in the User Guide can launch Comodo Backup on the HDD to restore files but I'm talking about a situation where one wants to restore to a new HDD. I'd like to be able to restore the image I created in question 1 above (with all partitions) to the new HDD.
Yes, you can restore to a new hard disk. If you use "disk, partitions and MBR" option in backup step 1, the disk/partition where restore is performed has to be equal or greater in size than the original.
3) Does the computer need to be ON at the specific scheduled time for the backup task to be executed or the task can be done anytime within the recurring time period (e.g. day, week, month, etc.)?
The computer has to be turned on for the schedule to run. You can use an option for the schedule to run at first chance if you want.
4) Can Comodo Backup resume from where it left off if the backup process is interrupted (e.g. if I want to shut down my computer)?
No, the backup will need to be re-ran.
5) I really like the self-extracting backup feature of your program. Can it self extract the encrypted backups, too?