Never heard of surge.sh, so I just tried it.
YES, you can host your website/demo/exercises/project here.
BTW, it seems it just serves static sites. I don’t think php will work, no databases, or anything.
You also can’t pick the domain you’ll end up with, (some-random.surge.sh) not unless you assign your own domain name to your surge.sh account.
I just uploaded my tribute page to surge, and it was pretty easy using the command line. The domain assigned to my project is “left-digestion”… which is assigned randomly.
Now, if you can spare $6/month, you can host at bluehost.com and you can host unlimited domain names, and also subdomains that you can assign yourself!
i.e. if you own mydomain.com, you can create: