Hey Kannan,
You can use the Shopify API to build the product pages (http://docs.shopify.com/api/product). Make sure you use pagination using (page/limit) parameters. You may also want to cache the API call somehow so you don't have to reach out to the Shopify API on each page load.
For the cart you have two options.
You can either create your own cart system and you use Cart Permalinks (http://docs.shopify.com/manual/configuration/store-customization/cart-permalinks) to create the cart on Shopify's end when the user clicks checkout. Cart Permalinks basically allow you to build a cart from a URL.
You could also craft custom Add to cart buttons that link back to Shopify. Sort of like a Buy It Now button: http://docs.shopify.com/manual/configuration/store-customization/adding-to-the-cart-from-a-remote-website The downside to this method is that displaying X items in cart on your PHP site would be difficult.
Hope that helps!
- Christian