Do I have to pay for a development card if I have a joker and the card needs only one type of resource?
From the rules:

Buying a development card
...
A joker token can replace any color.

This means that a Gold Joker token can be used in place of any single other token as part of any purchase.
In particular,

The Joker can be used to purchase a card from the center, not just the one you reserved.
The Joker does not replace all tokens of a given color, just one.

This second point is perhaps not quite clear from that rules quote, but the other interpretation would make them far too powerful. You can confirm that this is how jokers work by experimenting with them in the official app version of the game.