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 :)

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

My best guess is you have a lot of apps that open on startup that might be the issue but when you have more ram, you pc naturally allocates more ram to the OS to ensure smooth functionality, for example when I upgrade from 8 - 16 GB macOS went from using 4 GBto 6 GB maybe thats why? Also it could be some app using high memory like video/ photo editor. These are guesses at best tho

No they cannot charge you money for denying repair, in my experience there has been no 3 party store that can dent request. One possibility is that you gave in your MBP and they ordered the parts for it and after you denied repair but seeing from your post that doesnt seem to he the case. So i would go and get my money back