gearbox could be clutch issue but for me its always the synchros shedding teeth :( last box went like this, eventually could hardly get it into 3rd without a seriously long wait on upshift and literally no chance on downshift

coolant could be a million things. worst case its head gasket but check the oil cap for mayo and coolant cap for oil contamination. if theres none get a pressure check on the system done by a garage, may be able to pinpoint other issues such as leaking water pump, split hose, knackered rad or heater matrix, leaking stat housing etc etc