Broken hard drive or operating system
Question 1. see this link for how to.

1- Try a Safe Boot (hold Shift during start up)- (it does do some level of repairs).

2- You can try repairing the disk, using the Disk Utility, start with cmd-r.

3- If that does not work you can try to repair the disk using the Command fsck- fy

To get there start in single user mode (cmd-s) and enter that command fsck -fy to find out if it can repair the disk.

Question 2- 

you can use Target disk mode to recover files (you will need second Mac for that)