Honda Accord Euro 2005 Auto Engine Sound

So I'm going buy one of the used Honda Accord Euro 2005 Auto from an old guy, he seems to be honest and told me that the engine sound has been like this from day one. 14669 km on the clock. Here is the youtube link to the engine sound from the inside and outside the car.
https://youtu.be/AwtRNPBsAjQ (Inside)
https://youtu.be/tIlMGYpea0c (Outside)

After digging around the internet, I assume that this is the Alternator problem, the Alrernator is going to fail soon to be more precise. This is the known common issue with Euro serie I think. Have a couple of questions before buying this car:
1-This is just me assuming the problem is the alternator, but can anyone confirm that is it correct? Or there are some other problem could cause the engine to sound like this?
2-Is there any more common issues for the Euro 2005 that I should look for when buying this car?
3-There is also another common issue which is the Steering Wheel Pump leak. Any way or sign to predict the problem before it actually happens?

Any input would be appeciated. Thank you.

Alternator is possible with that sort of sound. Honda alternator is relatively expensive.

A few things worth checking. Air conditioner, door actuators (slow action-worn motor), inner CV joint (issue when accelerating), oxidised ground wire near battery terminal. Worth checking service history as well making sure engine oil, transmission fluid, fuel filter and spark plugs have been changed recently. There will be slight vibration felt through the steering wheel but excessive ones may be caused by bad engine mounts.

Does the sound go away when you turn the A/C off? Mine has that whining sound as well after I replaced the A/C compressor. It is there very clearly when accelerating with A/C on. It goes away when I turn the A/C off.

mine has a similar sound when started from cold but then goes away mostly when it warms up. Seems normal and has been like it since i got is (03 euro with 165k). Nonetheless, hard to say if it is the same sound as this one due to listening via recorded video on youtube...

I bought a new battery here and it fixed

That's a fairly filthy engine bay for 15000km.

Has he had it serviced every year?

If it hasn't been done it will need a fuel filter, transmission fluid change, brake fluid change, PS fluid change, coolant change, cabin filter and a few other service items. Count on $250-$350 plus labour (about 5 hours) if you aren't handy.

Low mileage vehicles aren't all they are cracked up to be. Machines are made to be used.