No they do not. However, SPCA will "lend" you traps for a small refundable deposit and you can bring the kitties there to have them spayed and neutered for free. There are also various organizations that will help with this, one used to be CatSNIP, not sure if they're still around. All cats need to be brought in cages for them to qualify as feral and to be snipped for free.
No
Exactly what Crystal said
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