"My father does not use a cellphone."
Translation:Benim babam cep telefonu kullanmaz.
This course doesn't teach spoken Turkish, it teaches standard written Turkish :) If you used kullanmıyor is would literally mean "My father is not using a cellphone." We have made it aware as much as we can that this may not reflect what you hear in spoken Turkish.
No, for two reasons:
a) "a cellphone" is not definite, and the accusative case is only used for definite direct objects (e.g. "the phone" or "my phone" or "that phone", but not "a phone")
b) the -u on telefonu is a possessive ending, and the accusative case on a possessed noun uses the buffer consonant -n- and not -y-, so "the cellphone" as an object would be cep telefonunu.