Re: TNR for a female cat
I had to do that once, TNR a feral female and let her go immediately after spaying. She managed to do just fine. She didn't run off and she kept returning for the food. It took a lot of time (around 3yrs, start to comfortable and relaxed housecat) and effort, but I did manage to tame and socialize her. She is my Pretty cat, who was TNR'd the winter of 2004 and is now a calm and happy housecat.
Overall, I'd say winter is the best time for TNR as it helps against developing infections warm weather can encourage. I still worried, I knew I wouldn't be able to catch her again to treat her if something went wrong, but I had to TNR her or be overrun with kittens. My experience was successful, the odds are great that yours will be, too.