If I make an international purchase with a card which contains domestic currency, is this currency converted to the currency of the seller? Let's say that I buy an app from the Play store. The seller quotes in Dollars, and I pay in Rupees (INR) --how does this transaction happen? 

Is my ₹ converted into $? Does this transaction also influence the forex markets (of course, negligibly --I'm only asking for understanding's sake). 

If I have to purchase a physical good while in the US, I'd have to convert my domestic currency into dollars and that'd push the dollar prices up since there is demand for more dollars. 

Does the same happen when I'm at a different country and purchase a good in dollars?
Generally the receiver bank / payment-gateway makes the conversion - except for currency accounts where the transaction is made directly into the account or if the sender chooses to make the conversion.

You can lookup the cutoff times for currency transactions on the different banks.