Your P/S belt may be slipping. If it does that, it gets glazed and slips even more. Is the belt glazed/and/or loose. If so replace the belt and see if it stops. Purge the pump by turning lock to lock several times while engine is running. Also, the fluid may be contaminated. The whine is from pump straining at maximun pressure (turning, usually at full lock). Not good for pump or hoses, seals as they may burst. If that doesn't fix it then your pump may be bad
A new belt is much cheaper that a pump. Suggest you change it, put an additive in the pump specifically made for them. Don't know what you have available over there.Bleed the pump as i suggested above. Verify that fluid is not contaminated. Dip a long screwdriver wrapped with a small piece of clean white cloth around it and scrape the bottom of pump. Muck or dirt means dirty fluid. Suction out the fluid and drain the lines. Start fresh. You should only use P?S fluid, not ATF fluid.
A pump in Finland is going to cost you big bucks! Do everything you can before concluding you need one. Over here its very cheap to just replace a pump. I would be interested to know how much there are over there. Let me know if you decide that route.
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