I would try a couple of things.
First create another user and log in as that user and see if any of your issues repeat. If they do then it is related to the system and not the User environment. If they do not there is likely a start up item for that user that is causing the problem.
Then reboot the Mac while holding down the shift key. When you see the gray Apple logo you may release the shift key. Boot could take a lot longer than normal, this is normal. Eventually the boot screen will show "Safe Mode.
Once booted and logged in operate the Mac and see if you can duplicate the issue. If not then there is either something that was installed or the O/S has become corrupted. See safe mode turns off all user installed things and some parts of the O/S to give you a working environment.
So if problems persist in Safe Mode, back up your stuff, boot into internet recovery mode and re-install the operating system. If it is not too inconvenient and you have a good backup and copies of anything you have installed I would reformat the HD and start fresh, just to be sure you clear any damaged/corrupted/bad files/apps.
The less fun part about now is that there may be a hardware failure. In that case make an appointment with a Genius at your local Apple store and tell them what you have already done. Be sure you back up your Mac before taking it to Apple as they could reformat the drive while troubleshooting your issue.
You may also want to post all the long descriptions of the apps crashing as it may help narrow down the issue further.