The indoor unit stops after 10 minutes and the remote indicators blinks. This auto stop cooling what do we do?

Impossible to answer as no one knows what this 'unit' is. All questions on Fixya need 'make model (what it is)' as the first three words. I will take guesses though. Then you have over 10,000 categories to choose from listed by 'make model.

E1 Error is used in many items, washing machines, dryers, fridges, dishwashers and even mobility scooters. Perhaps it is this as you posted to 'Heating and Cooling'?

The E1 error code is an AUTO-STOP PROTECTION indicating a short or open circuit in the indoor pipe sensor. Try unplugging the unit and waiting 2 minutes for the power to discharge. Then plug the unit back in.Apr 25, 2023
LG Air Conditioner - Understanding E1, E2, or E3 Error Codes ..
Videos just for fun!

I just checked the service manual and it is;
5 blinks - Outdoor power system

14.2.2 To Make a Diagnosis1 Timer LED starts to blink and the unit automatically stops the operation.
2 Press the CHECK button on the remote control continuously for 5 seconds.
3 "- -" will be displayed on the remote control display.
Note: Display only for "- -" (No signal transmission, no receiving sound and no Power LED blinking)
4 Press the TIMER ? or ? button on the remote control. The code "H00" (no abnormality) will be displayed
and signal will be transmit to the main unit.
5 Each press of the button (? or ?) will increase error code
number and transmit error code signal to the main unit.
6 When the latest abnormality code on the main unit and
code transmitted from the remote control are matched,
Power LED will light up for 30 seconds and a "beep" sound
(continuously for 4 seconds) will be heard. If no codes are
matched, Power LED will light up for 0.5 seconds and no
sound will be heard.
7 The breakdown diagnosis mode will be canceled unless
pressing the CHECK button continuously for 5 seconds or
operating the unit for 30 seconds.
8 The LED will be off if the unit is turned off or the RESET
button on the main unit is pressed.
Diagnosis
display Abnormality / Protection control Abnormality
Judgement Emergency operation Primary location to verify H00 No abnormality detected - Normal operation H11 Indoor / Outdoor abnormal communica
tion > 1 min after starting
operation Indoor fan operation
only • Internal / external cable connections
• Indoor / Outdoor PCB H14 Indoor intake air temperature sensor
abnormality Continue for 5 sec. - • Intake air temperature sensor (detec
tive or disconnected) H15 Outdoor compressor temperature sensor
abnormality Continue for 5 sec. - • Compressor temperature sensor
(detective or disconnected) H16 Outdoor Current Transformer open cir
cuit - - • Outdoor PCB
• IPM (Power transistor) module H19 Indoor fan motor mechanism locked 7 times occurance
continuously - • Indoor PCB
• Fan motor H23 Indoor heat exchanger temperature sen
sor abnormality Continue for 5 sec. O
(Cooling only) • Heat exchanger temperature sensor
(detective or disconnected) H24 Indoor heat exchanger temperature sen
sor 2 abnormality Continue for 5 sec. - • Heat exchanger temperature sensor
(detective or disconnected) H27 Outdoor intake air temperature sensor
abnormality Continue for 5 sec. O • Outdoor temperature sensor (detec
tive or disconnected) H28 Outdoor heat exchanger temperature
sensor abnormality Continue for 5 sec. O • Outdoor heat exchanger temperature
sensor (detective or disconnected) H30 Outdoor discharge air temperature sen
sor abnormality Continue for 5 sec. - • Outdoor temperature sensor (detec
tive or disconnected) H33 Indoor / Outdoor wrong connection - - • Indoor / Outdoor supply voltage H38 Indoor / Outdoor mismatch (brand code) H50 Ventilation motor abnormality 7 times occurance
continuously - • Indoor PCB
• Ventilation motor H51 Nozzle lock abnormality 2 times occurance
continuously - • Nozzle H52 Limit switch abnormality - - • Indoor PCB H97 Outdoor fan motor mechanism locked 2 times occurance
within 30 minutes - • Indoor PCB
• Fan motor H98 Indoor high pressure protection - - • Air filter dirty
• Air circulation short circuit H99 Indoor heat exchanger anti-freezing pro
tection - - • Insufficient refrigerant
• Air filter dirty F11 Cooling / Heating cycle changeover
abnormality 4 times occurance
within 30 minutes - • 4-way valve
• V-coil F90 PFC control 4 times occurance
within 10 minutes - • Voltage at PFC F91 Refrigerantion cycle abnormality 2 times occurance
within 20 minutes - • No refrigerant
(3-way valve is closed) F93 Compressor rotation failure 4 times occurance
within 20 minutes - • Compressor F95 Cool high pressure protection 4 times occurance
within 20 minutes - • Outdoor refrigerant circuit F96 IPM (power transistor) overheating pro
tection 4 times occurance
within 30 minutes - • Excess refrigerant
• Improper heat radiation
• IPM (Power transistor) F97 Outdoor compressor overheating protec
tion 4 times occurance
within 10 minutes - • Insufficient refrigerant
• Compressor F98 Total running current protection 3 times occurance
within 20 minutes - • Excess refrigerant
• Improper heat radiation F99 Outdoor Direct Current (DC) peak detec
tion 7 times occurance
continuously - • Outdoor PCB
• IPM (Power transistor)
• Compressor

Note:
"O" - Frequency measured and fan speed fixed.
The memory data of error code is erased when the power supply is cut off, or press the Auto Switch until "beep" sound heard following by pressing the "CHECK" button at remote controller.
Although operation forced to stop when abnormality detected, emergency operation is possible for certain errors (refer to Error Codes Table) by using remote controller or Auto Switch at indoor unit. However, the remote controller signal receiving sound is changed from one "beep" to four "beep" sounds.

Indoor unit indicator
RUN lamp = 6 time flash
TIMER lamp = Comes on
Outdoor unit indicator (LED5) = Stays off
Description of trouble = Indoor fan motor error (2)
Cause = Defective fan motor, Connector poor connection
Conditions of flashing = When air conditioner is operating and indoor fan motor is turned ON, indoor fan motor speed of 400 rpm or under continued for more than 30 seconds. (Air conditioner stops.)

MODEL NUMBER PLS AND BTU.... AND DOES ANY LIGHTS BLINK AT INDOOR UNIT... WHEN START UP....

At least it is cooling properly. U might just want to call Mitsubishi and ask them if it is operating normally based on your observations.

Possibly a bad control board in the outdoor unit. Pull the disconnect outside to stop machine, wait 10 seconds and out back in. White mist was likely frost built up on indoor coil due to condenser running without the fan.

If you need further help, reach me via phone at https://www.6ya.com/expert/thomas_092728000e6acb79

Just had the same thing happen to us with the same model (right on Xmas day).
Checked the circuit breaker is on in the fuse box. Power is on to the external unit. Filters are clean.
Internal unit activates... both indicator lights on. After 5 minutes blowing air it stops and the right indicator light goes out and the left indicator light blinks constantly.
The troubleshooting guide inside the internal unit (under the outer cover you open to clean the filters) suggests that 14 blinks is an abnormality with the external unit and refer to service manual.
Think we'll be calling a technician.

I'm not sure exactly what unit you have and what controls you have installed on the unit. But....there usually is a flash code schematic on the unit. Usually on the inside of the blower compartment cover. This should tell you what is wrong with the unit. It could have a low voltage short somewhere and is loosing the call for cool. So the answer can be a possible yes to your question but without knowing the flash code, it's hard to tell from my point of view. You might end up calling a service professional out to check it.

The operating LED will be blinking 5 times, means that there is a
comunication error (serial comunication) between the outdoor and the indoor unit.