oil leaks out the inlet

If the pump is "sucking back" oil when switched off, the inlet shut-off valve is not closing properly. I am not sure if this Leybold model actually has an "anti-suck back valve" or "inlet shut-off valve" but most direct drive vacuum pumps do these days. When you shut off the pump the pressure difference between your vacuum chamber low pressure and the atmospheric pressure on the oil in the oil box of the pump causes the oil to be pushed back towards the low pressure in he chamber. If the pump has no inlet shut-off valve, you should install one in the vacuum line between the vacuum pump inlet and the vacuum chamber. You should also allow the vacuum pump to return to atmospheric pressure inside the pump mechanism. This can be done by opening the gas ballast to allow air into the pump. You could also install and air admit valve between the inlet of the pump and the new shut-off valve. Most small lab sized direct drive vacuum pumps have a pressurized oil circuit. This oil pressure is used to open the inlet shut-off valve when the pump starts and on shut down of the pump the oil pressure drops allowing the inlet shut-off valve to close.