Yep, it's all GraphQL - I built the site a few years ago to play around with Apollo and AWS's serverless GraphQL offering and then it kind of snowballed from there.
Not much - I made all GraphQL requests GETs and cached them in CloudFront, which has some drawbacks but is pretty effective at keeping costs down because it allows Aurora to scale to zero as long as every request is in cache. The last week has been interesting (60,000 page views) and if things continue at that scale (doubtful) I might be looking at $60/month, mostly in Aurora costs. Most other months of the year had less than 100 page views total, nearly all cached, and it cost under $3 to run for the whole month.