No they don't.
Not sure. You may want to give them a call to find out. Also pretty sure they may have days when groups show up for those wishing to adopt them.
Correct @felix, however they do host kitten and cat adoptions. You can find more information on their website as to what days and what locations
No, they do not sell kittens. I've seen a guy outside of this store on the corner giving them away though.
Thanks! Your answer is awaiting moderation.