As for specs i would say seeing how your doing nothing laptop intensive i would say specs dont really matter, what i would say is to pay a little extra and get more storage, with you downloading a lot of photos and videos i would assume storage can be an issue but besides that even base model macs book pro can handle this very easily without breaking a sweat
This might be hard, but i believe its a logic board issue, again i could be wrong i am no expert, but at first i thought it could be the screen cable not being seated probably but, if it shows purple screen it could be anything from ram malfunctioning to an issue in the logic board, now it depends on luck if you have apple care good for you, but if you dont you can cross your fingers to to a repair shop and hope for the best. Also in case its a logic board or any internal issue it would cost a lot to fix. Hope this could help in some way :)