Codes without lights

[bg305]

I recently purchased a Foxwell NT530 since my innova 3100 j+ seemed to be absolutely useless with my 01s. I am also new to the car in general having only owned it for 2-3 weeks now, so i know very little of it's history.

In running a full scan of all systems I see the following codes in the scanner

Airbag System: id: 03 Description: DTC---Airbag warning supply

Alarm System: id 47, Description: DTC---Control locking synchronization
Alarm System: id 61, Description: DTC---Central locking limit position Unlock not reached
Alarm System: id 33, Description: DTC---Passenger compartment monitoring sensor
Alarm System: id 60, Description: DTC---Central locking limit position Lock not reached
Alarm System: id 42, Description: DTC---Wrong key or wrong transponder pill

What i find interesting is that there are no lights on my dashboard once the car is started (they all light up when i put the key in and turn it to run without starting). I think the foxwell can reset these but have not tried because I am a bit confused on why i do not see a light on the dash now.

Is it normal for codes to be stored without dash lights for airbag or alarm to illuminated?

-Brian