Tyre pressure control light is on, but pressure is normal.

I'm assuming this is about a rim size for a tyre? The tyre pressure will depend on a number of different things. The tyre size that is fitted, the vehicle it is fitted to, the weight it regularly carries and the average speeds the tyre has to cope with.
Most modern cars and trucks have a plate somewhere on the car giving the tyre size and recommended pressures for light load and fully loaded. It is often on a hidden panel.
Starting with the driver's door, open each door in turn and look at the area normally hidden by the door when it is closed. Also check inside the fuel filler cover.
There are plenty of online sites where you can look the pressures up if you have the vehicle and the tyre size.

Tyre wear is related to the load you put on your tyres and the pressures you run them at, many tyre suppliers have charts to show you visually why your tyres are wearing and what you should do. Low pressure and high pressure both stress the tyres more than the correct pressure. There is a guide to what pressure your tyres should run at for light and heavy loading, adjusting the pressure for a trip can also save fuel and improve handling. VW recommend 28 Psi all round for your 2003 Passat on standard Tyres.
The ASR light indicates that your stability control system is working, if it is just cutting in as you hit adverse conditions then it is working how it should, if it is staying on go talk to your VW Mechanic , there may be a fault, try turning the ASR button on and off on the dash.

I'd say the battery is flat on one of the sender units or has been damaged. If you have had new tyres put on recently take it back as they have more than likely damaged one of the sender units.

I can calculate it with spreadsheet I made, call myself tyre-pressure specialist nowadays.
Depends on tyres maximum load and Pressure needed for that ( AT pressure 6pr 55psi/3.8 bar, 8pr 65psi/4.5bar or 69/70psi/4.75/4.8bar). and maximum speed of tyre given as letter mostly N to R for caravans.

Then from Caravan MPVW ( max permissable Vehicle Weight).
Or better real weight ( overloading is more rule then exeption and unequall load is possible.

But normal car tyres or XL/reinforced/Extraload are sometimes OK if they have enaugh maximum load for MPVW.
Will try to make picture of example.

Depends also on the kind of tyre.
For the maximum load of tyre nex kinds need next pressure , wich is called AT-pressure/maxloadpressure/reference-pressure , for up to maximum speed of tyre or if lower 160km/99m/h. This is not the maximum pressure of tyre.

Normal car tyre /standardload AT 2.5bar/36psi ( exeptions as low as 2.2)
XL/Reinforced/Extraload AT 2.9bar/42psi ( exeptions 2.8 and 3.0)
6PR( plyrating) /C-load AT 3.8bar/55psi EUR ( USA 50psi/3.4bar)
8PR/D-load AT 4.5/4.8 bar/ 65/69/70 psi
From E -load is not often used in Europe.

From this AT pressure you can calculate the needed pressure for lower loads . Made spreadsheet for it in wich I first add 10% to the assumed load before calculating.
Will give example picture

32 PSI

Insert key press start button,push scrool on top of indicator stalk,untill you see tyre warning. Then press end of stalk to reset

This is the tyre pressure indicator. It shows that one of the tyres is losing pressure through a calve leak or puncture, or can also be triggered after you get new tyres or rotate the tyres.

The method to re-set the tyre pressure warning light is as follows:

Turn the ignition to position 2 (ignition on but motor not started). Press and hold the button under the handbrake until the warning light on the dashboard comes on for several seconds. Start the engine. Drive the car normally for several minutes. This will cause the system to re-set to the current tyres and pressures you have. It will then only turn the warning light on if the pressures change - for example if you get a puncture.

Honest advice ??Go to tyre shop and get the sensors removed and normal tyre valves fitted .This could cost a fortune if its a problem with electronics and encrypted software ,dealer only type job .

Using the indicator stalk, navigate to the tyre pressure reset option, press the reset button twice in short succession but hold it in the second time until a tick appears on the display