If the pump is tripping the GFI then could be a broken pressure chamber, which is were all the electrical components are and if it senses water it will trip the GFI. Solution will be to replace pressure chamber complete.

If the pump is turning on by itself then water could be draining back into the pump. Either the flapper inside the toilet tank is leaking water or the check valve on the discharge elbow is not closing all the way. Solution will be to inspect flapper on flush valve (inside toilet tank) or may need to be replaced. Also the flapper on the check valve must be inspected for obstructions of may need to be replaced.