Can my website have its own address, e.g. www.mywebsite.com?
Yes, your website may have its own address, e.g. www.mywebsite.com.
In order to use your own domain name you first need to register that name. You can buy a domain name at 123-reg.com for £2.79 a year.
Once you have registered your own name you can use it for your website and dinStudio email by following the instructions here.