Can we see a nanowire, whose dia is say 1 nm but length is 10mm, with naked eye? To see an object does at least two out of three dimensions must be greater than the minimum size one's eye can see?
no, a nanometer is much smaller than the wavelength of light, so you can not even see it with an optical microscope.
May be worth a note the "nano-" prefix is often abused in the literature. Things described as "nano" are often "really" micron sized. Additionally such small stuff often exists as agglomerates/mat/powder , etc. which then of course you can see if there is enough of it
No. Absolutely not.
Think about it. Visible light has wavelengths roughly from 400 to 700 nm. You are talking about feature sizes many times smaller than the wavelength of anything your eyes can see.
In addition to that, you certainly can't see things that small with a naked, as you asked about. Again, actually think about it. If you could see things even remotely that small with a naked eye, there would be no need for optical microscopes. Of course anything using visible light, which includes optical microscopes, are limited by the wavelength of light they use. Even the best optical microscope can't resolve 10 nm features, not even close.