Is it legal to build a website for a buisness and charge them without an LLC?

A limited liability company is one of many different forms of business organization.   Others include corporations, general partnerships, and limited partnerships.  There is no legal requirement that you choose any particular form for your business, either before or after you start operating, or indeed that you choose any form of artifical entity at all.  The two of you can simply do business as individuals. People choose to form llcs, or corporations, partnerships, or other artificial business organizations, for many different reasons, but the most important revolve around tax and personal liability questions.  While there is no legal requirement that you form a business entity to operate your business, there may be good reasons for doing so.  In terms of not violating any laws, I think you should be concerned more about copyright and trademark issues than issues about business organization.