RE: Ohio regulations?
Welcome to the Buckeye State. Yes, yes, yes and yes. Not only can you hunt squirrel with a rifle, in some parts you can hunt them with a handgun.
There is only one restriction on the type of sights you use: you can use a sight that projects a red dot. 'Laser' sights, that project the dot onto the target, are illegal. 'Red dot' sights, with which you only see the red dot in the scope tube, are legal.
The hunting regs handbook that you get when you buy a license is only a summary. The complete set of laws can be seen at your county seat, or just call the Division of Wildlife/your county Wildlife Officer. The numbers are in the book.
Good luck.