Macintosh HD disappeared from finder after "disk damaged and cannot be repaired"
I wouldn't suggest continuing to use an external drive for your MBP, apart from anything else it's just not practical.  

It seems like your internal drive has or is just about to fail.  Have you/can you check it's SMART status from disk utility?  Either way, I would suggest not worrying about trying to verify or repair it - just try and get your important files copied over to your external HD/other back up disk whilst you can still get some access to it.

Replacing a HD in a MBP is actually quite easy, ifixit: https://www.ifixit.com/Device/MacBook_Pro_13%22_Unibody_Early_2011 has good instructions.  

I have replaced a HDD in a MBP 2012 and would rate it as moderately easy.  Hdd are fairly inexpensive these days and tools to do the job properly are available readily from Amazon for only a few quid.