Any HDD sizes can be used for system running 24/7

If use RAID-5, all the HDD need to be in same size. You can add bigger HDD but it can only utilize same space as the smallest size HDD in the pool. SHR would be the better choice if mixes sizes HDD as it can maxed out the utilization.

If recovery, RAID-5 need to constantly read from the remaining HDD to do the rebuild, it create more stress to the remaining HDD.

RAID-1 when rebuild poses same risk as RAID-5 in that if another HDD failure it means all the data will be unrecoverable. That is why need to have multiple copies of backup for important data. 3-2-1 backup rule is always the recommended way. If your NAS data is always being use for read and write/amend, that is not backup, that is just your present data. You need to have at least another 2 backup, and one of the backup is stored in different place.

Like for backup photo purpose, do you think it's okay to turn on NAS only when you want to backup , then shut down for a period of time?

I heard this would hurt the hdd as nas hdd are meant for 24/7

I believe NAS HDD have same mechanism as normal HDD in starting and stopping the disc. So it's as bad as normal HDD that start and shut down. That said tho, I have read some people that say their NAS HDD died after 2 or 3 years because they shut down and start everyday. If you going to shut down and start everyday, might as well let it run 24/7. And if the system just going to run for short period of time to do backup, can get normal HDD instead.

I also have a NAS HDD that I use in NAS running 24/7 for 2 years then now move it to my PC that I shut down and start everyday, also 2 years. Still running fine. So I think really depends on individual situation. It might not be the daily shut down and start that kill the HDD but something else.