Are Verizon iPhones unlocked for use with T-Mobile 4G?

And if not, can an unlock make the iPhone work with T-Mobile.

Added (1). This is a Verizon iPhone 5

No.

Verizon is CDMA, T-Mobile is GSM.

You aren't physically able to unlock the phone, and you can't use a CDMA phone on a GSM network.

The verizon iphone 5 were sold unlocked at first, but it was corrected 3 months after release

Yes they are unlocked, However are not compatible with T-Mobiles 4g network which will result in coverage but absolutely horrible data speed… Edge network