*) Parameters for ajax refresh can be configured at System>Configuration>Sales>OneStepCheckout>AJAX update shipping/payment methods

*) Please select fields that your shipping and payment methods depend on, i.e. if your available shipping methods and prices depend only on country, select only country as ajax trigger. If any availablility or prices depend also on region, select also the region, etc.

*) Please note that on first One Step Checkout page load all ajax trigger fields on One Step Checkout page need to be changed (you need to enter value in them) in order to trigger ajax refresh.

*) In case shipping or billing prices, availability or extra fees do not display correctly, test the same address in standard checkout to make sure if this is a Magento or payment/shipping configuration issue or is the issue related to One Step Checkout. 

One Step Checkout is built on top of standard checkout and uses the same functionality. Standard checkout needs to work correctly. You can test standard checkout by adding a product to cart and going directly to http(s)://your url/checkout/onepage
You do not need to disable One Step Checkout for testing standard checkout.