umm.. your air conditioner is pushing air into your room? or is it in your room just cooling the air that's there?
If you are already pushing cooler air in, that's your intake.. if it's just in your room.. do you have an exhaust fan? If you do,you are likely fine as the negative air pressure will pull air in as well.
You can grow pot from seed in 3 months no problem. If you veg for 4 weeks and flower for 8-9(depending on strain.. I know some that go longer, but generally speaking flowering is only 2 months).. you can also go 12/12 from seed and have your weed done sooner, but if you're going to the effort, may as well veg for the month at least.
I don't know what your wet/dry season question is... if you can growing indoors, does that matter?