No, you don't have to if you don't want to, you can be self employeed and never have a real business setup. Some people say it is better, some say it isn't. Get a book and read up on it is the only way to know for sure. As well having a business kinda protects you from personal law suits in some way or another. Again a book would be the best way to start to get info on that or ask a lawyer
As for CC processing you dont need your own merchant account, you can use CCbill/Ibill/GLobill whoever you want and it uses their merchant account. They make their money from charging you 15% (or so) per transaction.
I think places like ynotmasters.com and adultnetsurprise.com have tons of information about cc processors and such as well as setting up your own business.
Hope this helps,
TheDoc