1. Does he also get the Bladed Bracers with my creature since the creature was equipped with it?
No, He does not gain control of the Bladed Bracers. Since you still control the Bracers, you could use their Equip ability to attach them to a creature you control. (Of course, you'll have to wait until you have the mana, and for the stack to be empty in a main phase of one of your turns.)
However, until you reattach the Bracers to another creature, they do remain attached to the stolen creature, and the stolen creature will continue to get the benefits of the Bracers (+1/+1 and possibly vigilance).
2. If the answer to the above is yes, does my opponent keep the Bladed Bracers if I played Unsummon?
Not applicable. They never left your control.