sabertoothed tigers.
The real scientific name for sabertoothed tigers of all ages was smilodon.
Sabertoothed tiger
yes
White tigers aren't a separate species, they're simply a Bengal tiger with an unusual fur color. As such, they'll happily breed with other tigers if they get the chance. In fact, being so rare, a White tiger in the wild would pretty much have to breed with a normal-colored one, if it is to have any chance of breeding. Holding out for another White - if tigers thought that way - wouldn't be an option.
Trying to breed them to repopulate them.
People can capture and breed the tigers and set them off back into the wild.
No Tigers are mainly solitary. They come together to breed and young tigers will remain with their mother while growing into adults, then they leave her.
Lions and Tigers have been known to breed in the wild. The Liger is the cross breed of a male lion and female tiger. The Tigon is cross breed of a male tiger and a female lion. While not common these do occur in the wild.
Trying to breed them to repopulate them.
because as it lived in the ice age it must have been adapted to the environment but as the ice age ended the tigers would have drowned into the melted ice or they were probably killed due to the heat and changes in the environment. It could have also had happened because most of their pray ( e.g mammoths) would have died so they could have had starved to death.
No such breed of dog exists. There local dogs in India that are used to hunt and track tigers, but not kill them.