A handful of domains will have restrictions on them, which means you can only purchase them if you meet certain criteria or have authorization (some examples are .gov, .edu. and .mil). But most extensions are available to everyone. In fact, most country code Top Level Domains (ccTLDs) are available for anyone to purchase, even if you don’t reside in the country in question.
It is also possible to setup a personalised or branded email address that simply forwards email to an existing inbox you may already have elsewhere such as Gmail, Yahoo or similar. This way, you can continue using your existing email address and receive your emails through your branded domain name. To send from your personalised address you will need an email mailbox account.