I've made an offer on single family home and included all the inspection contingencies. The seller responded with counter and terms the house is being sold AS-IS. It was Not listed as is, but obviously needed some work. 

If I accept the counter "As is", I understand it means I can't ask sellers for any repairs but am I still allowed to do all the inspection contingencies and negotiate the price in case there is major issue found during the inspection period? 

Here, yes....As Is simply means the seller is not agreeing, in advance, to make any repairs. Ask your broker, you should know this b