ok, id say the pressure system is probably ok, but without a rev counter its hard to know for sure. Check the wiring to the white pressure sensor with a yellow wire, pop the boot off and pull it back down the wire a bit make sure its in good condition, and make sure it isnt pissing oil out of it. May as well check the low pressure sensor as well, but that will never trigger the buzzer at any point. Make sure the wires are the right way round though, yellow -> white sensor, blue -> black/blue/brown sensor.
If that all checks out then I'd get another white sensor on there see if that sorts it. If not, you may really have low oil pressure! On a 1.3 both sensors are on the back of the head, worn cam caps can cause a low pressure condition here.
1st thing really though is to sort out the oil level, if it was me I'd dump the oil out and put a fresh lot in with a shiny new filter!