Hi Rezwan,
So it sound like you have paid for a lathe and they offered you this one.
If you turn it on, then you own it.
If you refuse it (due to surface rust and lack of manuals), then they will replace it with something else.
Is that right?
That's a tough choice not being able to turn a lathe on before buying.
That one looks fairly new (other than surface rust) so I doubt the wear is very bad.
Here's a few things you can do without power:
My favourite test for bed wear is to simply to move the carriage to near the headstock, tighten down the carriage locks so the carriage just moves, then try to move the carriage from one end to the other. Typically bed wear is worst near the headstock. However, surface rust may prevent this test from being useful....
For headstock bearing wear try lifting the spindle nose and listen then try moving it in a circle.
Ideally a dial indicator on a magnetic base can be used to measure spindle movement.
Here's a couple link to evaluating lathes:
http://www.mermac.com/advicenew.html
http://www.hobby-machinist.com/threads/a-guide-for-selecting-the-right-lathe-for-beginners.25915/
I wish you all the best luck in this!
Please let us know how it goes.
-brino