I want to integrate a 3rd-party Shipping in checkout process. Is this feasible in WIX?
There is no API yet for Wix Stores if that what you ask, that is still on the Coming Soon page so maybe it will come within certain time. Depending on the solution and the number of products you have you can always create you own smaller webshop and implement real time shipping this way.
You could use Zapiers Email Parser and parse the content of the order copy you get after sales, store that in a Data Collection and in that code shoot to real time shipping. I have tried that Email Parser and it works solid.
I have an account with a shipping services, they provide API to get the shipping quote based on delivery address and product dimension. I want to add that shipping price on checkout page in total amount.
What is the easiest way to do this?
As I said, if you use Wix Stores this is not yet possible because there is no API from Wix Stores to Wix Code. This is on the coming soon features page but nobody knows how this will work and what it will cover. So patience my friend...