Giving a Koran as a gift to non-Muslim friends: Is it permissible?

Apparently you can give. It is not obligatory upon non-believers to touch the holy Qur'an in the state of ritual purity. You must, however, be absolutely certain that your friend will not mishandle or abuse the holy Qur'an in any way. It might be helpful to educate him a bit about the most basic etiquettes of handling the Qur'an.

I do have my reservations about Md. Asad's translation. I have been told that his interpretations are at odds with mainstream.

If you have slightest doubt about your friend's ability and inclination to handle Qur'an properly, why not give him a classic manual on sufism, such as Imam Qushayri's Risala, Imam Hujweri's Kashf al-Mahjub, Sharfuddin Yahya Maneri's 100 letters, etc. (take your own pick). If your friend is destined for any guidance, then any of these works would be enough to draw him towards better understanding of Islam.