Can .onion sites have subdomains (e.g. subdomain.abcdefghijklmnop.onion/) or do the naming protocols prevent this?
It appears to have been suggested in 2012, and the developers (or someone) say they wanted to implement it. But I haven't seen anything else
Yes they can! For example, try http://whatever.bitmailendavkbec.onion which is the Bitmessage onion service with an arbitrary subdomain.
Not that the subdomain is not transmitted between the Tor client and the onion server. It's the browser that sends the full host (including the subdomain) to the webserver in the request's Host header, so protocols othe than HTTP(S) won't work.
At the moment it is not possible to have subdomains. Tor calculates the domain name of the hidden service from different parameters. To have a memorable, secure and global name would contradict Zooko's triangle and seems not possible at the moment.
