Service lights My RX is due for 10,000 service and it has gone slightly over. While driving today the engine light, AWD light and maintenance lights all came on along with the oil maintenance and AWD service message. Did this happen because there are more than 10,000 miles on the car and it has not been serviced yet?

The SH AWD uses electromagnetic clutch in the back drive axle to change the power distribution to the rear wheels. It would have nothing to do with the P0171 error. What TPMS valve stem was bad? Because this could be a clue to what the problem is. If a rear tire is having issues it could cause the sensor to make adjustments to the system to compensate for the tire. The person that changed the TPMS might have also caused the issue when they worked on the tires.

Page 13 of owner's manual says:
AdvanceTrac
(if equipped):
Illuminates when the AdvanceTrac
system is active. If the light remains
on, have the system serviced
immediately.
AWD locked (if equipped):
AWD
Illuminates when all wheel drive
LOCKED
(AWD) is engaged/activated. If the
light continues to flash, have the
system serviced.

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ALL WHEEL DRIVE (AWD) SYSTEM (IF EQUIPPED)
Your vehicle may be equipped with an All Wheel Drive (AWD) transfer
case. With the AWD option, power is supplied to all four wheels
automatically with no need to shift between two-wheel drive and
four-wheel drive. If your vehicle is equipped with the AdvanceTrac
stability enhancement feature, you can change AWD modes, if desired,
by selecting AWD options through the message center.
For the lubricant specification and refill capacity of the AWD transfer
case refer to Maintenance and specifications chapter.
If your vehicle is equipped with AWD, a spare tire of a different
diameter than the road tires should never be used. Such a tire
could make the vehicle difficult to control as well as result in damage
to driveline components.
Utility and four-wheel drive vehicles are not designed for
cornering at speeds as high as passenger cars any more than
low-slung sports cars are designed to perform satisfactorily under
off-road conditions. Avoid sharp turns or abrupt maneuvers in these
vehicles.
The following sections, Normal operation, Autolock operation and
Disabling AWD, apply only to vehicles which allow the driver to change
AWD modes through the message center.
Normal operation (vehicles equipped with AdvanceTrac
During normal operation:
• the AWD system is in AWD AUTO mode (AWD LOCKED will
illuminate in the message center for four seconds when you first start
your vehicle). The AWD LOCKED indicator in the instrument cluster
will also come on.
• AWD AUTO mode can be overridden by pressing SETUP in the
message center. When you first press SETUP, AWD <AUTO> will be
displayed, then if you press RESET within four seconds of pressing
SETUP, AWD <LOCKED> will be displayed. AWD <LOCKED> provides
power to all four wheels constantly which allows you to operate your
vehicle in severe winter or off-road conditions such as deep snow, ice
or shallow sand. It is not recommended that you use AWD <LOCKED>
on dry pavement.

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• AWD <LOCKED> can be cancelled by pressing RESET in the message
center. (The AWD LOCKED display in the message center will then
turn off and the display will return to AWD <AUTO> for four seconds
when the shift is complete.)
Autolock operation (vehicles equipped with AdvanceTrac
If the AWD system begins to overheat, the system will place itself in the
Autolock mode:
• the AWD LOCKED indicator light will illuminate in the instrument
cluster and AWD DISABLED <LOCKED> will be displayed in the
message center.
• AWD LOCKED will be displayed in the message center for four
seconds and a warning chime will sound. This condition may clear
without any action being taken by the driver.
• the AWD LOCKED indicator light in the instrument cluster will turn
off when the AWD system cools down.
• When the system is sufficiently cooled down, AWD AUTO RESTORED
will appear in the message center for four seconds and a warning
chime will sound.
Disabling AWD (vehicles equipped with AdvanceTrac
When a problem is detected in the AWD system:
• the AWD LOCKED indicator light in the instrument cluster will flash
eight times every two minutes in the message center.
• The message center will then display AWD DISABLED for four
seconds, then SEE OWNER'S MANUAL. A warning chime will also
sound. The warning displays and chime will continue until RESET is
pressed (which will clear the message from the display).
• AWD LOCKED can still be engaged by pressing SETUP (the message
center will display AWD <DISABLED> LOCKED), then pressing
RESET. The AWD LOCKED indicator light will illuminate in the
instrument cluster and the message center will display AWD
DISABLED <LOCKED>.
• To disable AWD, press RESET. The system will go back to AWD AUTO
mode momentarily, then the AWD LOCKED indicator light will flash in
the instrument cluster eight times every two minutes. The display will
then show AWD <DISABLED> LOCKED for four seconds and then
turn off.

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• If a serious problem occurs with the AWD system, the AWD LOCKED
indicator light in the instrument cluster will flash 10 times every two
minutes. The message center will also display CHECK AWD and a
warning chime will sound. You can press SETUP to check the status of
the AWD system (which will display AWD <DISABLED> LOCKED),
but the AWD system will be disabled until the system is serviced.
Driving off-road with truck and utility vehicles
AWD vehicles are specially equipped for driving on sand, snow, mud and
rough terrain and have operating characteristics that are somewhat
different from conventional vehicles, both on and off the road.
When driving at slow speeds off-road under high outside temperatures,
use 1 (First) gear when possible. 1 (First) gear operation will maximize
the engine and transmission cooling capability.
Under severe operating conditions, the A/C may cycle on and off to
protect overheating of the engine.

Just to be clear, your maintenance light has illuminated and not the check engine light (CEL) . a CEL indicates that the car has detected a problem of some kind and depending on the severity of the fault it may be harmful to continue driving.

If it is the maintence light then that is easy. It is automatically set to come on at predetermined mileage marks to remind you to have the car serviced.

The maintenance required light is a reminder to bring the car in for scheduled maintenance (every 10,000 miles). The light will flash after start up for 10 seconds once you are 2000 miles from the car's scheduled maintenance. Once you pass the scheduled maintencance mark (every 10,000 miles) without having the maintenanced performed and/or the light reset by the dealer, it will remain on forever unless reset.

To reset it yourself
Hold down the trip meter button, turn the car to on, wait about 20 seconds, start the car, and let go of the button. Light is reset until the next mileage interval.

*make sure lo beam headlights are turned OFF during the procedure*

I’m happy to assist further over the phone at https://www.6ya.com/expert/jeremy_cd01d4e4178e5a11

to reset, push odo buttom hold until put key on w/o start engine several seconds

The maintenance light is to let you know when your recommended services such as oil change, filter replacements and so on are due. if you want to reset the light i think all you have to do is push in and hold the trip odometer peg until the light resets or about 10 to 15 seconds. The light should flash a few times then go out. Do this with the key in the ignition and in the "on" position without the engine running. Then start the car and make sure the light is gone.

It means you have reached the mileage for service. Once the service has been done, they will have to reset the light.

What really happens is your service check indicator light switches itself on due to completion of 10,000 or 5,000 Km (depending on the manufacturer's specs) from your previous oil change or service. The internal clock keeps track of your mileage travelled and let you know when the 10,000 or 5,000 km is up. All that is required is to RESET the service indicator light. On some cars, the resetting of the service light can be done by the car owner which normally involves pressing a button at the front Instrument Panel and so on and so forth. If you have the user manual for your car, I suggest you read it to see if there is anything on resetting the service light.
The bad news is not all vehicle manufacturers have a reset button at the front dashboard, and some requires the use of a Diagnostic Scanner to do this. Ask your mechanic if you are not sure.
The speed is cut down to 60 is due to the fact that if you continue to drive your car after the prescribed mileage without changing the engine oil, there will be 'accelerated' wear and tear to your engine and perhaps even an early engine overhaul. Driving with a long overdue engine oil change is bad but driving it at speed would be worst. I believe you get the drift.
As for your mot test, it is mandatory that no warning light whatsoever should appear at the instrument panel but yours showed up.

simply it's time to take it in for a dealer service...it may mean anything from a simple oil change to an timing belt replacement.  Which I think is due at 60k

Disconnect the battery and reconnect.
This should clear the computer memory.
This may cure the problem.
Suspect extreme cold primary cause in transmission?
Good Luck !