As frankenduck has mentioned, the charge battery light is on when the ignition key is turned to On. The light is on because the battery isn’t being charged. The battery isn’t being charged because the engine isn’t running to operate the alternator to commence charging. If the engine is running but the charging light doesn’t light, that is happening because the wiring of the charging system could be somehow faulty if the battery light has been proven to operate.
As he also indicated, the oil light is on when the key is turned to On because the engine isn’t running to produce oil pressure.
The temperature light is off when the ignition key is turned to On because it only turns on when the engine overheats when running.
There are several videos on YouTube that explain how to use a multimeter to check engine electrical systems. Watch a few of them. You should prove by testing that the two year-old alternator is caput, not assume that it is, or you should take it to auto electrician for diagnosis.
Some of this could possibly be ground problems, as you have indicated. You could find them using a multimeter.