I have never heard that we have to carry the credit card with us while traveling. It might depend on the airline but l have traveled plenty of times when my husband used his credit card to pay for my ticket and l didn't have it on me and it was no problem.
Also, no! You don't need visa info to purchase a ticket but if l WERE YOU l would track the flilghts prices and see if they are stable l would buy it later, with the passport on hands! But if the prices are going up too quickly, yes, go for it! Just my opinion