If you're losing power steering you definately have a voltage drop somewhere. It is electric and once the voltage drops too low it shuts off the pump.
If it is the alternator I'm sure you could pick up a used one cheaply and get it fitted for not that much. It sits under the car driven by the aux belt which also drives the water pump IIRC. If it is an older shape W168 then they can be had for about £20. If it is the newer shape then I think they are watercooled and are a bit more.
Start the car and stick a voltage meter on the main battery - it should read somewhere around 14v if the alternator is healthy.
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