A lot of kernel problems

I would suspect you might be having intermittent problems with a failing SATA hard drive cable to your SSD. Here are instructions on how to replace it:
https://www.ifixit.com/Guide/MacBook+Pro+13-Inch+Unibody+Late+2011+Hard+Drive+Cable+Replacement/7655

A way to test:
Remove your SSD and place it in external 2.5" drive enclosure.
Connect the external and boot to see if that helps/solves your problem. It will of course be slower since you are using USB 2, but you should not be getting kernel panics and be able to install things.

 

Have you run the Apple Hardware Test (your Mac is a 2011 device)?
https://support.apple.com/en-us/HT201257

I experienced exactly the same issues as you're describing with my late-2013 rMBP. One day, a KP while browsing the web and they got more frequent over 10 days until I couldn't keep the Mac running reliably, and finally gave up and ran a hardware test. The Apple Diagnostics tool (for 2013 and later Macs) led to the discovery that a memory module and another motherboard component were failing - Apple replaced the motherboard (with its soldered-in RAM) and all has worked since.

 

I agree with this. The symptoms sounds like what's likely to happen with bad RAM rather than what would happen with a bad SATA cable. Unfortunately, the memory test utilities supplied by Apple have historically not been particularly thorough and will often pass RAM that fails other tests. If your machine is capable of booting Memtest86+, that's a much better one (except that in some Macs, it instantly fails good RAM, since Apple failed to mark the memory addresses as read-only). Otherwise, you can run the memtest command line app that's bundled inside Rember from single-user mode.

 

From the reported 4MEM/9/4000000 error, it reads to me like one or more failed/defective RAM modules...