Car overheats and shows Check coolant level even after we fill-up.

Car overheats and shows Check coolant level even after we fill-up. I checked the Fan is working and Pump turnning. I suspect Thermostat.

Also, when idling it starts to shake(a bit like mis-firing)

I check diagnostic codes (see below) cleared the codes and checke 5 min later again here are the list of diagnostics before and after clearing.
Thanks for any assistance.

Before clearing codes:
ABS C1287 Hist - Steering Sensor Rate Malfunction
DDM U1713 Hist - Loss of Front Door Module to Window Motor High Speed Comm
DIM P1536 Hist - Engine Coolant Overtemperature - Air Conditioning (A/C) Disabled
IPM B0429 Curr - Temperature Control #3 Rear Circuit Range/Performance
IRC u1016 Hist - Loss of Communications with PCM
PCM P0741 Curr - TCC System Stuck Off
RIM C0660 Curr - Level Control Exhaust Valve Circuit Malfunction

After Clearing
DDM U1713 - Loss of Front Door Module to Window Motor High Speed Comm
IPM B0429 - Temperature Control #3 Rear Circuit Range/Performance
RIM C0660 - Level Control Exhaust Valve Circuit Malfunction