Yes, definately strip and resand, otherwise the fresh paint will chip.

Either sand or use a paint stripper. But if you use the stripper, you should still sand. When you sand, you open up the grains for the paint to stick to. And you really should use primer first. So if i were you, use stripper, sand, primer, then paint. I work in a cabinet factory doing this everyday. Only with cabinets.

Yes you have to sand them down and then u have to primer them since they were stained before so the stain does not bleed through the new paint.

Yes you have to sand the old off or it will end up a mess with cracking, and splitting of the paint.
Your might check the phone book or newspapers. there should be a furniture refinishing place near you which for about 10 bucks each would dip your chairs in a vat for removing the old paint and stain completely,. Just becareful and wear gloves using any paints, stains removers, and keep away form kids.

Also a friend used oven cleaner and scrubbers to remove old varnish and paint from an old mantle.
Apply and allow to set over night and try it.

wash them with soap and water using a soft cloth such as an old towel or wash cloth to remove the chalky dust, since that is what it is. you'll need to keep running water to let the dust fall off, then allow to dry thoroughly, preferab ly in warm sunlight. once dry, dust them off with a clean soft cloth to remove any residual dust left behind. then do the preperation and re-paint. use an oil-base rather than water base paint. the house type for exteriors would be best.
if you sand it, use a fine sand-paper and make sure you get the dust off afterwards. the paint will adhere better

You never said if they were metal or wood, since they are outdoor chairs I'll presume they are not wood. First you will need to sand them, not to remove all the paint just to rough up the finish so the new paint will stick. Then wipe them down with mineral spirits to remove dust and contaminants. Prime any bare metal with a good bare metal primer. Paint with a good exterior metal paint. Personally I've had great results with Rustoleum, but no matter what you use, several light thin coats are ALWAYS better than one or two HEAVY coats. If your gonna take the time to do the project, do yourself and favor and do not rush the last step, take your time. You'll be glad you did!

Yes, sand them first.