Yes, all exhaust comes with the mounting bracket(s) unless otherwise stated, usually if you derestrict the exhaust and are fitting it to an otherwise standard bike you will need to change the rollers, clutch springs and main jet size for it to run at its best.
For Piaggio 2-stroke with standard carb and airbox as a general rule you would drop the roller weights by 1.5g each and upjet to 68-70 (6mm dellorto jet) and remove the brass plate from the carb mouth (if it hasn't been removed already).

Usually if you are fitting it to an otherwise standard Piaggio you need to change the rollers and main jet. As a rough guide fit 1.5g lighter rollers as a starting point, increase the main jet to 68 and remove the brass plate from the carb inlet mouth if it hasn't been removed already.
Unless your drive belt is worn then you won't need to replace it if you don't want to. 

Yes if you want it derestricted you can add the exhaust derestriction to the basket as well when you place the order, there is a red button on the exhaust listing to add it or you can follow this link:

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If your Piaggio Zip is completely standard apart from the new pipe and you derestrict the Stage6 exhaust, usually people use a 62 if the brass restrictor plate is still fitted in the carb mouth between the carb and airbox, or a 68 jet if the brass plate has been removed.

This only applies if you are still using the standard air filter and airbox.