The answer to your question depends in part on why you are asking. For example if the oil light is on that can be an indication of low oil pressure. It can also mean the sender has failed and is giving a false reading. If the oil filter is clogged it can also reduce oil pressure. You would want to check the actual pressure with a real pressure gauge to see what the actual pressure is.
On the other hand if you have the engine all apart on an engine stand and you are in a convenient spot to change the oil pump. Then you would want to measure the clearance between the gears and the oil pump body. Also check the end play of the gear to cover. If it is out of spec you would want to replace it. For that matter if you are doing a full overhaul you should probably replace it along with all the other new parts.
You will need to run an oil pressure test with a pressure gauge.
either your oil pump screen is clogged or you need a new pump
may need an oil pump may need a motor
Need to know which fluid pump, there are several such as, water pump, oil pump, power steering pump, fuel pump, windshield washer pump, they all pump fluid.
Zero oil pressure.
Loss of oil pressure.
As far as I know ALL cars have an oil pump. Every car I have ever worked on has had the oil pump INSIDE the oil pan.
You will have to remove the oil sending unit/switch and screew a oil pressure gauge into it's place and then start the engine and read the oil pressure.
Loss of oil pressure.
Of course, there is no other way to get at the pump.
From The Information You Have Asked. You Have An Engine. There Is No Engine That I Know Of Where The Oil And Water Run Together. So The Answer Is NO. You May Want To Change Your oil After You Get The Engine Back Together And Running. But No You Do Not Need To Drain The Oil Out To Change The Water Pump.
when puting a oil pump in a motor u always need to prime the pump manually and check it screen