Sorry, had to check some of theses in game. Apologies for vagueness.
Sensor range = default without skills is 800m. So the increases seem to be built off that, BAP increases that 25%. No clear "this is your new range in meters" sadly.
With Stealth Armor turned on -
Enemy: Cannot target/target lock you unless you get hit by TAG, a NARC pod or some flavor of PPC just like how ECM is disabled. Active Probes, UAV and counter ECM cannot see Stealth Armor 'Mech/negate it. Enemy can see you visually only, Stealth Armor hides your heat signature too, so you appear like a shutdown 'Mech on thermal vision too.
But...
You: You cannot spot for your team, cannot target R unless at literal point blank touching range and worse you cannot see what you team is targeting. So Aff your BAP isn't doing jack if you have Stealth turned on. You can spot with TAG, NARC and of course UAV.
NARC pods light up enemies unless they are under ECM coverage even without line of sight, so making them useful even if you team doesn't have lurms.