Is it possible to hit your own men with normal weapons?
I know you can damage your own men with rockets and grenades, but when firing your regular weapon is it possible to cause friendly fire?
I've had a few situations where two troops were close together and when the soldier lined up to shoot the bullets (or energy) passed very close (or maybe something through) another unit to the target.
I know in the original X-COM friendly fire was definitely possible.
No, there is no friendly fire with "normal" weapons assuming the unit is friendly (e.g. not mind controlled or panicking). You can blow up a friendly's cover, though.