how can I buy an iphone on a payment plan outside the US?

Apple has no store in Guyana.

For payment plans you would need to contact your local credit card issuer, or cellular carrier and see if they have any plans there if they sell iPhones.

The link provided by askbarnabas is for the U.S. payment options only.

For Guyana see here: Apple - Guyana - Find Locations

You cannot get Apple Card outside of the US but there are financing options here - Financing

Nowhere. Apple does not sell screen replacements in any way shape or form. They only replace the screens themselves when required.

Any screens you find online will be in the best case, screens salvaged from other used iPhones, or in the worst case fakes and reproductions.