Hey @loginname, @sdayman,
The page also looks fine to me, in four browsers I’ve tested it, including iOS Safari. The only thing I’ve noticed was that Dev Tools pointed to two CSS files, the ones @sdayman noticed as 404s, as not loaded for being mistakenly attributed the wrong MIME type. (Though when I try to open them in a separate tab, they do return 404s) Not sure if one of them would affect the slider:
It would be good if you posted your test domain you say is a copy that doesn’t use Magento, so we compare after any clues.
As far as caching goes, your HTML is not being cached by Cloudflare.
As for the Cloudflare Browser Cache Expiration, keep in mind that for any asset that CF caches, it will still respect the origin headers if they have greater values. So if your origin says to cache CSS for a year, Cloudflare will not change that, but if it says to cache them for 1 hour, CF will change that to the default, in your case 4 hours. In case you need to force users to purge the cache, you would have to rename the files in question. (EDIT: Or add a query string to them, like …css/?ver=123)