When throtling and transmission is shifting low oil pressure stop engine appears across the message center

The IPC illuminates the LOW OIL PRESSURE indicator in the message center when the powertrain control module (PCM) detects low engine oil pressure, and the signal circuit is low. The IPC receives a class 2 message requesting illumination message from the PCM.
No it can't shut down the engine !
No

The engine bearing clearances expand with heat which, if excessive, will lower the oil pressure. The spring in the pressure regulator in the oil pump will cause the pressure to drop for the same reason. A partially plugged oil intake screen will work in conjunction with the oil pump to cause it too.

Fist check oil level, the sensor is a pressure switch worked by oil pressure, hopefully the sensor has gone faulty. The oil pressure needs checking, if the oil pump or relief valve has gone faulty, the engine is being starved of lubrication and is causing internal damage. It is advisable NOT to run the engine till the pressure has been checked. (hope it's the sensor)

Could be the oil pressure sensor. It stops the engine if oil pressure is to low.

it means the oil pressure is low and may be low enough to damage the engine if you keep drving/running the engine. it would help if you could tell us the actual oil pressure, engine and mileage . basically, the oil pressure may be low enough to wreck your engine, then again it may be bs......

If you rev the engine does it go away? What is probably happening is that you have damaged or worn engine bearings. These bearings are designed so that there is a gap(clearance) between the crankshft and the bearing. This gives a space for the oil to pass through. If the clearance is too big the oil will pass through too quickly and the oilpump will not be able to build up pressure, even though the volume of oil pumped is sufficient.
When the oil is cold it is thick and the sensor sees the pressure as normal. As the engine oil heats up it gets thinner and that causes the pressure to drop. Also the lower the RPM the lower the pressure. I would suggest you get the oil pressure tested at a service centre ASAP. Also have them test the sensor although sensor failure is rare. Low oil pressure will not just go away and causes more damage the more you drive increasing your repair bill considerably.
I'd say you are already in for a cranshaft regrind and oversize bearings. Perhaps (if you're lucky) only just an oil pump although this is unlikely as bearings tend to fail before an oil pump does. I'd replace both at the same time since the engine has to come out for both these repairs. The cost of having the engine out a 2nd time far outweighs the saving on spares when doing both the first time.

Check oil level via dipstick , if it is full check oil filter is not blocked (You need to have a mechanical knowledge to do this ) if both ok then oil pump is on its way out or there is a blockage in the engine oilways

Check your oil, it may be low if not the oil pressure needs checked. The sending switch could be bad or you have low oil pressure. If you have low oil pressure have it fixed ASAP. The loss of oil pressure can cause severe engine damage.

go to autozone and get the codes. they will test for free.

Message Center Display
The following messages may be displayed on the message center.
This message center will display CHECK TRANSMISSION if the following codes have been set.


DTC Codes Possible Faults P1746, P1747, P1760 Electronic pressure control solenoid P0743, P1767 Torque converter clutch circuit P0750, P0755, P0760 Shift solenoid circuit P1714, P1715, P1716 ISIG P0731, P0732, P0733, P0734 SFT error P0741, P1742, P1743, P1744 Torque converter clutch error P1783 Over temperature P1700 NEV error P0712, P0713, P0710,
P1710, P1713, P1718 Transmission fluid
temperature error P0705, P0708, P1704 Transmission range sensor error P0500, P0503 Vehicle speed sensor error P0715 Turbine shaft speed error
NOTE: For codes. For additional information, refer to Diagnostic Trouble Code Chart.

code p 1870 refers to transmission component slipping
That can be from dirty oil or a clutch pack or band slipping or low oil pump pressure in the transmission
you say that it occurs on highway driving after 2 hours and that slipping will add friction heat to the transmission oil bringing on the oil temp light
take it to an accredited transmission professional service center that works on your make of vehicle , have the oil changed which require the pan removal
at the same time that will allow the adjustments to be done
when reassembled and refilled , have a pump pressure test done