"Any sense provided by cyberware can also be provided by this power"
Can Adept have a) Spatial Recognizer b) Ultrasound Sensor with Adept Improved Sense?

a) Yes.

b) I'm not 100% But, I believe it came up that it says somewhere that you can have Ultrasound the last time I was arguing about this on here

What about a radar sensor?

What, like having the senses of a bat? Sonar?

I am not entirely sure... but in SR3 i think it was mentioned that a Ki-Adept can aquire any naturaly accuring sense. So Echolocation or maybe those electrosense of some fish would be ok (Or tremorsense of worms). But radar... nope.

I would keep it that way... the internal radar is not really senseware. It is more of a specialized sensor. It even needs it's own computing power and doesn't use the wearers brain.

And the magic guys allready have pretty much all advantages... give the techguys a bit too *g*.

Sonar is Ultrasound vision.