I firmly agree with you on the travel policy. I an in the position of having to make travel arrangements constantly...I have a corporate card to do it with!
I too have NEVER heard of a company requiring an employee to pay for their own travel w/their own card.
I also agree with you regarding the other finances...Confused, you MUST protect yourself right now financially. Don't get stuck holding the bag! It's tough right now, but do the logical/sensible things in order to protect what you've worked for.