I have a goodman furnace model number gms80904bncc. When the temperature in house is met the blower continues to blow. Even if I put the thermstat in off mode the blower is still on

The relay for the motor is stuck or the points inside the relay are arced closed. Replace the relay.

check on door pane, inside or outside if will tell u what code 2 means

It is possible it is a problem with the motor mounting bracket or the fan housing itself. Tough to believe you have gotten three bad blower wheels. Also could be the motor .

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your limit switch is opening up, that causes constant fan. Check for flashing codes after flame shuts off and fan continues. Check airflow, filters, lack on return air for possible hi temp limit problems.

If it makes the noise before the blower comes on it would be the exhaust fan. If it makes the noise when the blower comes on then I would say either the blower motor or bearings to the fan.

Usually when the furnace blower motor runs all the time
The limit switch or rollout switch is usually open or bad.
The furnace board is seeing that one of those switches is open, so it brings the blower on to try to get the heat out of the combustion chamber area, so the switch will close. But if the switch is bad and won’t close, the furnace board will keep the blower running continuously.

Depending on the age of the furnace you may be able to adjust the cool down. On some furnaces there is a silver box usually made by honeywell. This is your fan limit control. If you take the cover off you will see a dial with different temperature settings with 3 pins in a grove. The first one is fan on with temperature rise this turns the blower on when the furnace starts and warms up. The second is the fan off after furnace shuts down, this would be the one you want to adjust to a higher temperature to keep the blower from blowing cold air. The last pin is the high limit if the furnace gets to this temperature it will shut the furnace off but keep the blower running. Make sure that the thermostat fan option is set to auto and not on.

Yes. If the high limit is tripped, the furnace will bring on the fan continuously until the limit resets. Often, they will not reset if tripped repeatedly. If the furnace is too large for your application, you probably are not able to move enough air to keep the heat exchanger cool enough.

69,000 btuh is adequate for a 12-1400 square foot house.
Otherwise, your thermostat simply tells the furnace to cycle on/off.
If it calls for heat and does not come on, the problem is with switches and relays within the furnace.
Your setting the temp higher only causes the other parts to keep trying until they finally light and heat.
This is based on your information saying it will cycle on and blow cool air--not hot air.
You will have several temperature variations from floor to ceiling.
You probably have ceiling vents as well.
You need a technician to verify the rollout switches, fan relay, inducer fan etc. if the furnace is not firing everytime you call for heat.

At what point does the pilot blow out? Within 5 seconds after it lights or when the room air blower turns on?