Yes, you can opt for dedicated IP address by paying $2/domain/month.
Yes, we do provide domain registration service. You can register your domain along with our hosting packages.
No, It is not required for you to have a domain to apply for a hosting account. But if you are purchasing hosting and are going to build a site that you want visible on the internet, then you will need a domain.
We do not have any limits on emails, but you yourself can change this settings as per your own requirements.