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You gave a ton of good information in your question, and that cuts down on my need to ask you a lot of questions in return.
The key piece of info is that you said t he charger light sometimes looks very weak. That tells us that your magsafe charger adapter is beginning to fail. It needs to be replaced.
Now depending on what exact model and version of macbook pro you have. You either need this power adapter http://amzn.to/1NOPwgj
Or this one. http://amzn.to/1JE7tZ4
Before ordering either though, reply and let me know the year and the size of your macbook pro, that way we can be certain were ordering the exact charger you need. Also, I would stay away from generics, the 20-40$ you save on a generic charger, isnt worth the damage it can do to your 1500$ + machine.
I strive to provide great service, and greatly appreciate a rating of excellent ( 5 stars ) selected and submitted below this answer or at the top right of the screen. I always answer follow up questions.Dustin S.Senior Technician and Network Switching Systems Operator / Maintainer.
The charger is failing.. Thats the root of your issues. The crashes can be fixed, and were caused due to the failing charger.
To fix the crashes, you either need to reset the pram, or repair install the OS. You could reset the pram as follows.
Shut down your Mac.Locate the following keys on the keyboard: Option, Command (⌘), P, and R. You will need to hold these keys down simultaneously in step 4.Turn on your Mac.Immediately press and hold the Option-Command-P-R keys. You must press this key combination before the gray screen appears.Continue holding the keys down until your Mac restarts, and you hear the startup sound for the second time.Release the keys.
Just keep in mind, no amount of software "fixes" will fix a failing charger. ( Identified by the light getting faint and flickering)
Dustin S.Senior Technician and Network Switching Systems Operator / Maintainer.