Why both "ul" and" acesta" .is it possible to say: băiat acesta?
No, you need to add the article "-ul" to support "acesta". In Romanian you also need an article at the end of the noun, not just the pronoun "acesta", compared to English where you use "this boy".
What a difference between Acest băiat and băiatul acesta?
There's no difference.
Thanks but what's a variant commonly useful?
Both are pretty common. There is also a third variant: "băiatul ăsta" (also common, but less formal), which is really a shortened form of "băiatul acesta".