Shipping via fedex

I am considering using Woocommerce. We currently ship via fedex, however the shipping is fixed based on the number of items in a particular category. Ie 1-15 is $13 shipping, 16-20 is $15. Would I need to install the fedex extension for this?

In the future, we would like to add some other products and the cost of shipping those would be based on weight of those products. So if someone purchases some items from the fixed shipping category and the other categories the shipping would be fixed + live rate = total shipping. Is it possible to do this with any extensions?