Laws on motorized bikes

The laws are different in every state, dude.

Yup... every state, and sometimes every county or city will have their own set of laws as well as whether or not they choose to enforce them... I know here in San Antonio they tend to be pretty lenient as long as you're not being too annoying... I remember once when the state auditor came by my shop and saw mine he started asking questions about the bike and I took the opportunity to ask him what the rules for these were here in Texas. .. he told me it needs to have functional pedals, keep it below 125cc, and keep the speed at 30mph or below. I told him I don't have a problem with 2 out of those 3 and he said just keep it under the posted speed limit and nobody should mess with you... the street I ride on most has a 35mph speed limit and traffic usually flows at 40 to 45mph so I just blend in with the traffic and haven't had any problems.
this culd be the same for out on the beaches, but they may have a different set of rules out there too... maybe if your lucky you can find someone to ask, but pretty much as long as you stay under 30mph and don't have super loud exhaust you shouldn't have any problems.

Yes.... I have a few helmets... full face style as well as a half shell helmet... I usually wear the full face in the colder months but if I'm going for speed I'll put that one on as well... I go helmet less if I'm just going to put along to the store down the street but if I'm headed to my favorite taco hut for breakfast I'm going to be doing between 35 and 40mph to keep up with traffic so I prefer the extra protection of the full face there too...

You can wear just a regular bicycle helmet if you wish, but since I got motorcycles, I got motorcycle helmets so I wear them out of convenience...