How old is the furnace. Did it work perfectly until this recent set of problems. Any new construction or changes to the furnace.
The voltage and ground error may be due to a loose connection. Turn off the furnace at the main breaker box and check all 120 volt connections including the switch at the furnace. Check the hot (black), neutral (white) and ground (bare copper) for any signs of a loose connection. Check the connections at the furnace control board. If you're comfortable with electricity, I'd check the connections at the main breaker box making sure the neutral and ground wires are bonded securely.
Now turn on the power BUT do not call for heat. See if you get the improper main ground error now.
If the board shows no errors set the thermostat to 5 degrees above the house temp. Now go to the furnace and watch it run. You want to see if the burners shut off while the main blower keeps running. Then you want to see if the burners restart or if you get the high limit error. If the burners shut off then you know you have either an overheating heat exchanger or a faulty high limit switch. If you check the furnace installation manual you will read about the expected temperature rise through the heat exchanger. It's usually around 60 degrees. So if you measure the air temperature as it immediately leaves the furnace and subtract the house air temperature (air temp into the furnace), you want a number less than 60 (or whatever your manufacturer says).
If you determine you do not have inadequate air flow through the heat exchanger (temp rise is too big) you'll need to look at the duct system and especially the returns to see all are adequately sized. Another possible option is change the blower speed but you need to know your duct system can handle increased air flow, which I doubt.