Site collections do not have parents, they are always at an equal level in a web application. The URL /sites/ is a managed path under which site collections are created, the 'root' of the web application is a separate site collection.
(you can create a 'portal' which creates a logical link between site collections but there is no true hierarchy created here, only clickable links in the navigation. site collections remain separate entities when you tie them to a portal).
There is no documented number to the maximum number of site collections, however if it's slowing down, consider putting some on separate content databases, as this will greatly help backup and recovery procedures.
EDIT: I didn't read that document well, the documented limit of site collections is 250,000 per web application, but I personally think this is a soft limit, and if you have problems over this value the first thing MS will tell you to do is to move some of the site collections to another web app.
EDITEDIT: As I've came across this confusion before, I've decided to write a blog post about this distinction. You can read it here.