“I hear you” could also be “I hear ya”, a slang expression meaning “I understand you”, “I understand your situation”, or “I empathize”.

No, it's not "old English", it's still in common use today.

This sentence is often used by counsellors and psychologists to reassure people that they are being listened to, but it has become an overused and meaningless expression

I hear what you are asking and I understand it. :P

I would say yes to this question. I have used "I hear you" the same way I would use "I understand you". It is usually used when someone has just told you some information or explained something to you that you may agree with.