Rethink your question... it sound idiotic.
By having sex. All animals become pregnate through sexual intercourse,
YouTube.com
Yes. Dogs are not selective with sexual partners and do not have compunctions against incest. To suggest that they will avoid mating with closely related dogs is projecting human morals onto animals.
get them fixed at the vet
cold water
yes
About 5 to 20 min ... is a normal mating duration.
Yes the well trained Bengal cats and Boxer dogs usually stop on their own when mating.
Hard to imagine their mating rituals being called dances, but yes, they do.
Try YouTube.
The as the other dogs.
Dogs and cats will not mate together.