Re: Adwords free coupon
Welcome to the AdWords community :-)
Please see the article "Using promotional codes and coupons" where it states-
"Promotional codes (also known as coupons) offer a monetary credit to an advertiser's account. Typically, they're given to new advertisers as a helpful way to get started with AdWords. If you're a new advertiser, you might be eligible to receive one."
You cannot apply to get a free coupon but as stated above they are sometimes given to new advertisers. PLease be aware, if you should receive one, there is criteria to be followed for redeeming it, again this is outlined in the article I have added.