fictitious business name, license, and LLC

Hello,

I live in California, and I plan on moving a few times in the next
year before moving to Washington state. I am starting a web hosting
business and the business does not need a physical address to operate.
I plan on using my parents address as the main business address for
tax purposes and operate mainly from a home office to start. My
parents place is in a small town and does not require a business
license, but the city I live in does.

questions:

1) Is it alright to operate this way without getting a business
license in the city I live in. I'm in an apartment at the moment and
it is more of a pain plus all the moving I'm doing....

2) I'm considering using my name. If I use my last name 'only' do I
have to file for a fictitious business name in the following case:
i.e,  'Norman Media' or would I have to use my full name.

3) If I do use my name; and I  use say "xyzhosting.com" instead of
NormanMedia.com, will I have to file a fictitious business name for
"xyz Hosting" even if I state on the bottom of the website that "xyz
Hosting" is ran by "Norman Media."

4) and... should I form a LLC for liability protection since I may be
dealing with a large number of customers on a monthly basis

I appreciate your impute and advice,

Regards,

Brent