Yes this can be used on a refinished bathtub.

No, heat is not required to make good contact for the bath mat. The tub surface needs to be completely cleaned and dry before applying bath mat. It is also important that the adhesive back of the mat does not come in contact with your hands as this may have an effective on the adhesion to the tub.

The bath mat needs to be peeled off of the tub. You need to run some hot water in the tub in order to loosen the adhesion from the mat to the tub and then peel the mat from the tub.

Yes this bath mat can be adhered to the bottom of a non slip floor and the shower chair would be stable. Please ensure that the floor is clean and dry in order for the bath mat to adhere properly.