MacBook Pro Lion Recovery Cannot Reinstall
Most of the problems seem to be coming from having the wrong date (and possibly not having internet access).

You might as well zap the PRAM. If you have problems, see here.  Then be sure you are connected to both power and internet when you reboot.  If necessary, set the clock manually.  

The issue with the screen, well, it depends on how hard you're pressing and which model MacBook you're using, but it is not necessarily unusual.  

UPDATE: I've been reminded that one cause of computer slowness is a failing hard drive.  Sadly, despite S.M.A.R.T status reporting, it's very hard to be sure if a drive is failing until it has completely failed.  See if you can boot off an external drive and compare the performance.