I've put 6 games in my cart and went to check out but when I click on the button to go to check out it brings up a log in page and when I put my password in the page just reloads as if I never clicked the checkout button at all leaving me still on the list of games to add to my cart

Maybe there are some server issues as it should not ask for a password during such things.

if one of those games was the new staints row then yes its the Gog server and a known issue at their end