Ditto above post. See if local humane groups will spay/neuter for you and if it costs anything, it's usually far far less than at regular vet offices. This is a golden opportunity for this because the kitty will probably be trap-smart after this and you can impress this fact on the groups in case they are not engaging with you as much as you'd like. If you really run into a dead end with humane groups, Friends of Animals offers low cost spay/neuter certificates that participating vets accept (google Freinds of Animals and you'll find the info) - I have done this numerous times to try to help cut down on the number of breeding (and therefore likely starving) kitties out there in the world.
As for the chickens, I would be concerned about small chicks. Usually they'll leave adults alone but there are exceptions to this reported here on BYC.
JJ