How long will the scar after waxing will last on my face? How should I get rid of it quickly?

Depends. Waxing shouldn't cause scars, but you may have post inflammatory hyper pigmentation, which is usually a reddish or purple discoloration. This will generally fade with time, but bleaching creams like hydroquinone, retinoic acid creams and steroid creams can help it to resolve more quickly. You will want to use sunscreen, as sun exposure will make it worse.