Calliper mounting bolt spacing should be pretty much the same, otherwise there’d be all sorts of issues marrying callipers to different frames/ forks. If you are swapping 160mm zoom for 160mm tektro then there is no need for a calliper adaptor plate, these are typically used to fit bigger rotors so the calliper needs to be spaced out for the larger diameter braking zone.
the rotors themselves are not all the same fixings, so you need to check the mounting points and bolt hole locations
have you thought about trying a larger 180mm rotor on the back, and just spacing out your current calliper ?
swapping one 160mm brake set up for another doesn’t seem like a great move unless you think there are inherent issues with the zoom set up.
as posted in your other threads a change of pads may resolve your issues, the current pads could have been contaminated during build
/ set up, an errant spray jet of lube would vastly reduce the effectiveness of a set of pads.