You can own hunting rifles. What you hunt is up to you.
A "sniper rifle" is simply any high powered rifle with a scope. Any 30-06 would do just as well as the military 30-06 and they are "commonly" used for Deer, Bear, Moose, Elk, and many other types of large game animals.
As far as I know if you have it for hunting purposes then yes. But you need to check with your local laws.
Coldnt be further from the truth ..shakes head ..as If !