HI Creedon,
I am facing the same issue and have been thinking of redirecting to a payment page from Squarespace cart. I am not able to use Stipe and Paypal since both are not tailored for Indian customers and two major Indian payment methods (UPI and Internet banking) are absent.
The questions you have raised are my concerns too. I want to use Razorpay payment gateway for the checkout. Razorpay has an API, will that help in my case?