Al-jawab billahi at-taufeeq (the answer with Allah's guidance)
Engagements in Islam is permissible. However, One is not allowed to meet or talk after the engagement. The purpose of engagements is a promise and confirmation to marry. At that stage, the boy and girl are still strangers to one another in that they cannot communicate with one another. Hence, Interaction between a non-mahram man and woman are not acceptable in Islam.
Also, there is no point in having a prolonged engagement, it is better to perform the Nikah as soon as possible and then one can therefore, interact in a 'Halal' atmosphere.