First thing to try is a Safe Boot. Hold Shift down at the startup chime and give it much longer to boot than usual. See how it behaves there. If it's OK, then boot normally and check. If not, then start using Disk Utility.
Also, open Console in Utilities, go to system log and Diganostic Reports (both of them) and check for any messages from around the times of these events.
Sounds like a failing hard drive, which happens all thee time as hard drives fail all the time, or you have a bad drive to logic board cable. Which on Apple Mac computers happens regularly.
you need to take it to an Apple store to be checked out and fixed.