I have an old Vigilant woodstove with an 8 inch pipe. I would like to use 6 inch chimney pipe, i.e.. Reduce the pipe diameter from the stove up to the roof. Is there any problem with this: draft, safety, etc?

Why reduce? Is this an existing gas flue? Since woodstoves can burn much hotter than a gas or oil heater and produce creosote, you should use an approved chimney system for wood stoves. These have special safeguards for roof and ceiling penetration. In may areas you will be required to have a spark arrestor too. Make sure your homowners insurance will cover a wood stove installation.