Whenever I hold up one of my snakes in front of my Siamese fighting fish's tank, both parties look like they want to eat the other! I'm sure given ½ a chance a snake would snap up a fish in a second. As for finches, I don't see why not, they eat quails and chicks, so why not finches. I'd just be concerned if they were it's primary diet that they'd not get all the nutrition they need as a finches body weight is pretty low and a good proportion of it is made up of feathers which don't give that much nutrition.
I had an idea a while ago that my uncle should get a childrens python or 2 to keep his finches under control. I gave him 10 finches and a huge aviary a few years back when I left Australia and since then, the aviary has been extended and joined onto another one and the population has exploded to 300+. Even blocking off the nests and removing others hasn't curbed them and giving away handfuls to friends and petshops doesn't make a difference and it's costing him a fortune in feed -so I figured that he could keep a pair of pythons and feed them 1 finch a week when they're small and perhaps move up to 3 finches a week when they're bigger...they are part of their natural diet after all!
As for the crickets...whoever told you that baby cornsnakes eat crickets should be strung up by their toes and flailed....baby corns should start on tiny baby mice and if they're too picky for mice, they might be tempted by lizards, but crickets are not part of their diet.