If it is a particulary cold chimney then insulation will help keep the flue gases warm and improve the draw.
No, you can only only use a gas liner for a gas appliance.
If the correct fuel is used and the flue swept reguarly the liner should last 10 to 15 years.
Most stoves are 5 or 6 inch, however some can be 7 or 8.
Cowls should be fitted to prevent rain, also birdguards will prevent debris in the flue.