Thank you for your inquiry. Allow me to quote your questions and provide the answer for them :
1. I want the Standard package. I can register one domain. Is it any domain?
Yes. You can register one domain. I'm not clear about 'any domain' but the domain you're registering with us is the domain that we will provide you the support. If you register domainA.com, we will only provide support for domainA.com.
2. If I have full access to the code, is the exception a link back to jomsocial.com?
I apologize as I am not quite clear about this question. For JomSocial Standard, you will have a 'Powered by JomSocial' link in your community page. Would you be kind enough to elaborate more on this question?
3. Could I use any other database besides mySQL?
No. JomSocial only supports MySQL.
Please elaborate more on your question so that I am able to help you understand JomSocial better. Hope to hear from you soon! :)