It is normal that I repeat this lesson already two months?
( Sorry for my english )
Would it change if you were to say: "We are giving him the phone"?
Not really, although potentially you could say that 'the' means almost the same as 'this' and translate it as "ten telefon".
Doesn't komórkę work here?
Well, as almost all phones nowadays are cellphones - ok, added.
Why isn't 'Podajemy mu telefon' accepted?
Well, "podajemy" means that we pass the phone to him.