MBP system reports 2 disks while About this Mac->Storage shows one HD?
You clearly have two separate devices: one a 5400rpm rotational hard drive, and the other an 'after-market' Intel SSD of 160 Gb.

There's limited space in an MBP, so is it possible that your optical (DVD) drive has been replaced with a housing for an SSD?

If you set Finder preferences to show hard disks on the Desktop, does the SSD show up?

Crashes could be caused by a defective SATA connector, either to the SSD or to your hard drive. These parts are known to fail: you can buy replacements very cheaply. If the connector to the SSD is failing, that might also explain why it's missing.

With a 10-year-old mechanical drive and a possibly failing connector to a third-party SSD installed in the optical drive bay, you might want to open it up, replace the hard drive with a new, large-capacity SSD, and investigate any physical problems with the existing SSD and housing.