1) Yes you can! but keep in mind that laptops tend to get hot and fast. As for memtest, i run mine from a bootable USB, this might require going into the BIOS and changing boot priority.
2) Hibernation "locks" up about 4-16 GB of space on your drive while shut down obviously doesn't. Its a matter of prefrance, my laptop runs a small SSD and every GB matters to me, so my hibernation is turned off. Other than that there is nothing stopping you for hibernating if you need it.