I understand that Network Solutions is, and has been under investigation for some time now by ICANN. The wheels of justice grind along slowly.
Here's a TRUSTED source to check out your domain names (new)
http://instantdomainsearch.com
As far as registration, I use 3: GoDaddy, NameCheap and Name.com
Most anytime you want to change registrars, the registrar you want to move TO will handle this for you. Nice thing about that is, you usually get the service for a fairly low price, and it includes a year's registration.
Pete