Koi really need a pond 12ft long by 6ft wide and 4ft deep or larger, if the pond is smaller than this then you should probably considering rehoming the koi and getting goldfish instead, as koi have the potential to grow to 3-4ft long.
They're omnivorous fish so do best with a little bit of everything in their diet, including veg, variety is the key to a good fish diet, koi generally eat most things goldfish can and do (i.e. bloodworms, artemecia, krill, cooked de-shelled pea's, chopped up blanched spinach, chopped up prawn, fish flakes & pellets etc). During the winter months, if the pond's temp falls below 10degree's C, you should stop feeding the koi food (they can actually go for weeks without food during cold weather, if you feed them when the pond is too cold, the fishes metabolism will be very low and it won't be able to digest the food properly/quick enough, which can cause the food to rot in the fishes gut and/or make the fish constipated, which can be a lethal condition in fish)- if you have to feed them anything during these cold times, it should only be small quantities of wheatgerm (which you can buy in most pet shops).
Does this pond have any filtration and what is its dimensions/measurements (length, width, depth)?
The pond may also possibly need a clean if the previous owner never cleaned it out, fishing out any dead leaves or plants in the pond is important- if there are any pond plants in the pond, some of these may need cutting back as well
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There are many diseases and parasites which can make a fish sick- keep an eye out for any physical symptoms like: scales sticking out on end, small white or black spots, large white/gray splodges or growths (particularly ones rather cotton wool-like in appearance), bloody streaks or blotches, torn or ragged looking fins, eroded looking mouth or fins, white/stringy looking poop, swollen/inflamed/red looking gills, threads hanging off fishes body, fish lice, worms coming out of fishes bum, cauliflower or flesh like growths on fish, ulcers etc. Also keep an eye out for behavioral symptoms as well, like: rapid/labored breathing or gasping at the surface of the water, fish flicking/rubbing/itching itself against objects/stuff in the pond, fish shaking/vibrating, fish losing its balance/appearing like it doesn't have the ability to control its direction etc
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Stuff like fountains should be turned off during the winter as they reduce the temp of the pond too much.
but to feeding them im not sure about. i know they eat well but depends on how big they are etc
