How do I repair headphone jack on a cassette walkman?

Hi,

I got an Aiwa HS-G35MKIV Walkman. Overall it is in a good condition but the headphone jack is bothering me. I have two problems and I try to explain it as good as I can.

First problem:

It is supposed to be stereo. When I plug it in (a little bit) sound comes out of the right headphone pad, when I plug it all the way in it comes out of the left headphone pad.

Second problem, and the one that bothers me the most: When I listen on my headphones there is a weird noisy sound. It comes out of the headphones and sounds like a mixture of hissing and high frequent tinitus (fieping / pipeing). When I turn up the volume to max it is unbearable. When I lower it I am getting used to it but still annoying me. When I turn down the 10kHz on the equalizer it also gets a little bit better. When I get the 3.5mm cable a little bit out of the headphone jack and but a certain kind of pressure on it the noise disappears. I believe that maybe the headphone jack is a little bit loose and I want to fix it. Hope someone is able to help me.