There are a few other factors, but yes, it's safe.
No a falcon will only breed once in the spring.
all Pokemon can breed more than once as long as you put it in a daycare with a ditto. some Pokemon cant breed which are the ones that don't say if there a boy or girl.
Yes.
yes
no it is not
Yes
Yes, if there's more than one bull around, or if the bull trailing her is very promiscuous.
Yes. I have done it more than once.
You can breed Lucario with Ditto or trade for more, but you can't actually catch any more.
Yes, once you beat the elite four you can breed it.
Mod Loader is the only mod that will allow your client to run more than one mod at once. It is very safe!
Yes & no. You can, actually, get mono more than once. Although not many people get it twice, you can & people do, so be safe regardless.