1. Am I right to think that I am not subletting, given that a subletter is someone who occupies the premises while the tenant is not there, but I am in fact here?
The NY Court of Appeals said:

"[A] sublease is a transfer by a tenant of only part of his estate or interest in the whole, or in a part, of the demised premises, with the reservation unto himself of a reversionary interest in the leasehold estate"
http://scholar.google.com/scholar_ca...en&as_sdt=4,33

Your roommate gives you money in exchange for living there. Your roommate is your tenant. You are subletting. Make no mistake about that.

And it certainly appears that you haven't complied with the sublease statute:

http://law.justia.com/codes/new-york...ticle-7/226-b/

2. Am I right to think that I do not have to supply my roommate's identification, but merely inform the landlord of who my roommate is?
You're correct that the cited statute (235-F) in paragraph 5 says inform the landlord of the name of any occupant within 30 days.

However, paragraph 8 says:

8. Nothing in this section shall be construed as invalidating or
impairing the operation of, or the right of a landlord to restrict
occupancy in order to comply with federal, state or local laws,
regulations, ordinances or codes.
Which tells me that the landlord may be able to require your roommates ID under federal immigration laws. I can't say for sure but you might want to check on that before you push back too hard.

3. Lastly, am I right to think that it is not legally possible for a landlord to prohibit you from entertaining any guests at all in your apartment?
That's true. A landlord cannot prohibit you from entertaining guests in your apartment assuming, of course, that you are not making a lot of noise or disturbing neighbors.