Most Helpful Guy
I think his asking you if he can call your son his son is weird. There's nothing wrong with him liking your son, and it's great that he treats him well. That's all good. But your son is most definitely NOT this guy's son. If you and this guy ever became like a real couple your son would be this guy's girlfriend's son.
Most Helpful Girl
I'd say yeah, he sounds more into your son - or at least into the idea of having someone he could be emotionally invested, but always while remaining 'superior' and 'in control', as you would be with someone much younger.
mind you, it took him ONE MONTH to say 'thank you for the bbq'.. really?
the fact you never spent any time alone, just the two of you, sounds weird indeed.