will the trans out of a 97 olds bravada fit into a 96 chevy k1500?

The 700R is the original name for the 4L60. GM switched to electronic controls in '92 making it the 4L60E, a common trans in half-ton trucks and some three-quarter-ton trucks. So unless your truck just happens to be one of the few half-tons with a 4L80E, you should be golden but you may still have issues with the different shifter setups.

Maybe. The '97 Olds has a 4L60E, The '96 K1500 probably has a THM700R. If both have the factory engines, the Olds has a 4.3 and the K1500 has a 5.7. Mechanically they MIGHT mate at the converter, however their shift assist systems are entirely different. So, with a lot of effort and $$$$ you may be able to make it work.

same engines your ok if not then will have small problem with rpm's due to the stall speed with the torque converter wiring will be ok if 4x4 then you must stay with the k1500 t-case the k1500 is a 4x4 the bravada is an all w/d that is different

The 4.3 L engine will bolt up to any small block chevy v8. so yes the tranny will fit. may not be as strong, but will work if you need it to. All electronics may not hook up either. but it should drive.