The ones that stick on your window are brilliant and the birds are pretty safe there AND you get a brilliant view of them feeding. Remember cats can shin up trees very quickly and easily. This time if the year and the coming months are when the newly fledged chicks are about and they are not street-wise and are easy prey for predators. Make sure your feeders are near cover (a nice thick bush) so that they can hide quickly when danger appears.
Regarding the woodpecker. Green Woodpeckers will eat freeze dried ants eggs that are used for fish food. You could sprinkle those on the ground where it usually feeds.
Enjoy your birdwatching, it will give you so much pleasure. Oh, and if the cats are a nuisance, get a dog:-)