You may use jack chain for the application, however, we cannot make a specific recommendation as we do not know the look you are trying to achieve. Please be aware of the weight of the pots and the working load limit of the chain.
Smaller. The smaller the number the larger the chain.
I doubt the chain would hold up to intense heat. It is a light-weight chain.
I would use and eye screw it the ceiling then attach the chain with an s hook. You could bend the eye hook to accept the chain directly and by pass the s hook.
Probably not, you will need to grab a worker in the store or you can cut it yourself most times.