Well, the bad news is, you're a bit lost and you seem to have chosen a host which is either slow, non-responsive, or there is a problem getting email from you to them or vice versa.
It really isn't supposed to be this much of a mystery, even if you are completely green (which you seem to be).
A bit of general info, just to put your mind at ease...
You have requested a domain name (URL). This will be registered at a registrar. The registrar needs to know the nameservers for your domain (your host will provide you with nameserver info and most likely runs this server).
Nameservers point your domain to the correct server that your web site files will be on (in your case, Invision's server).
Registrar > Nameserver > Server where your site is
That's nutshell.
Once your domain is actually registered (I'm not certain that it has been yet, doesn't seem to be exactly), then nameserver info will need to be updated and it will take a couple of days before all servers world-wide will update and everyone will be able to type in
http://www.parrotloveinternational.com and *bing* magically your site will pop up.
It isn't encouraging that your host (Invision) isn't replying to you, and that surely isn't a good sign of things to come. If it comes down to it, you should cancel that service and sign up with a host which does reply to your questions.