A broken rod must be replaced. Most rods are made of carbon and can not be repaired. The same thing for wooden rods. If your repair them they will remain a weak spot and will snap soon again. Rods can be bought by your local kite-dealer.
Sometimes you find tear in your sail. This can be repaired so you don't have to worry that you kite is lost. There are three ways to repair the sail:
1.)You replace the whole panel of the sail. This is not a good option as you only weaken the edges of the other surounding panels.
2.)Sow a patch over the tear. This is also not a good option as you weaken the surounding sail.
3.)The best way to repair the sail is to stick a sticker over the place. This sticker is made out of the same material as your sail but with only a sticky side. You can get this by a well assorted kiteshop.For cheap kites made of PVC you can use sellotape. For kites made out of cotton or similair fabric you use of course the same material.
If the tear is to big you end up with the other options or to replace the sail.
NOTE: If you are repairing a single-liner you must also place the same patch on the other side of the kite on the same place. This is for balance as well as for the look.
Your lines can be repaired if they are broken. Not with a simple knot, but with a splice. If you reapir with a knot you'll actually weaken the line, but with a splice you can gain back 85%/95% of the original strength. The modern lines are made of Dyneema, a very slick polymere. They have a hollow core. To repair the line you'll need a sleeveneedle. For the rest you have to follow the drawings.