Your pump is running on 240 ("230").
Ideally the pressure switch would have been mounted "closer" to the pressure tank. The symptom not having a close enough connection would be to turn off early or some such. Your symptom about starting the pump by pushing the contacts is not caused by that however.
If you had not already replaced the pressure switch a few times, then we would expect a bad pressure switch. So now, get the multimeter. Numbering the switch terminals 1, 2 , 3 , 4, then the voltage between 1 and 4 will be about 240 volts plus or minus maybe 10%. That should be about the same whether the pump is running or not.
When the switch is closed (on) the voltage 1 to 2 should be less than a volt. Same for 3 to 4. If this is found not to be the case, you have a third bad pressure switch.
Also, you want to read up on setting and checking the air precharge.