I am currently interviewing for a position with a new company. I would like to reach out to past employees on LinkedIn for their honest feedback about the company and the position itself. Is this OK to do?

Yes it is. But most will not answer if they do not know you. The best thing is to see if any of your connections have connections that can get you to someone who worked there.

Yes but also when the new company sees you are doing this... you may expect to lose the offer.