You will likely raise a flag somewhere if you publicise what you are doing, but I highly doubt there would be any issues if you're working on this in private as a hobby.
As for chemicals, I can personally vouch that it is a terrible idea to order reagents (or even chemistry equipment) as an individual. I tried to teach myself organic synthesis in the summer before starting my doctoral studies, and ended up with MIB searching my house. Certainly on a list now :(
Please tell me there is a blog post or something documenting this experience. Sounds like a fun read.
LLC or nonprofit, with a business address. At least for bio reagants, they won't ship to you otherwise.