Well, guess you need a bobcat:laughing: if all the flying critters are not getting the job done.
Size of cat (fat, lazy) will be determined by how you feed him. We feed our neutered (before we got him) cat dry cat food, free choice, and he brings in mice, rats and rabbits all the time. Feed him from a can or your table scraps, he'll put on lots of weight.
Neutering is not a mandatory thing....although it will reduce his wanderings and fights if neighboring male cats are around.
You've got a great cat there from your description....it's your friend now and will remain so...you've got a good deal, he poos outside, feed him in your barn and give him opportunity for shelter, he'll find a place he likes, may not be the one you make for him, but if he'll find a place that suits him and is good for him. It will move around depending on the weather. typically it's a place with a view so invaders, be they rodents or otherwise, are seen and taken care of. In terrible weather, he may choose the insulated spot you have made for him.
Not all cats are equally good mousers....some are FAR more interested in hunting than others. If you see it has caught something, he may bring it to you...means he's proud of it and showing it off to his family/pride, meaning you, so you should praise him and play with it a little bit and let him know you are appreciative of dead chipmunks. Do this in the barn and you may find you are cleaning up remains of chipmunks regularly.
You say you have lots of chipmunks, may take more than one cat to reduce population since they reproduce quickly. Have you thought of a pellet gun? In my experience, cats that decide they like you and stick around are really good to have. Got two of them myself. Leave them with claws, for sure.