Will I be protected against HPV after my 2nd shot of gardasil?

Not completely. Studies have shown that full immunity and complete benefit is only achieved in individuals who receive all three injections of the Gardasil vaccine. The vaccination schedule is at 0, 2, and 6 months.
Not likely. You need all 3 shots within one year to build up your immune system to recognize and fight off the hpv infection/exposure. Getting two doses may benefit you, but 3 doses are necessary to fully protect.