I can see why this might have you worried - it's never nice to think about someone you've had a prior bad experience with being your boss. However as things stand it is your response and attitude to the new situation that seems the more likely source of future problems.
I basically think that he lied, as claiming to hold a grudge could jeopardize his ...
There are a lot of assumptions about your future relationship with your new manager in your question. Sometimes it is helpful to realize, that a past relationship does not define what will happen in the future.
It seems that you are content with the situation for now but you have some doubts and fears about the future. Therefore it is best to do your job to ...
Preemptive complaining won't get you anywhere. You expect professional conduct from your new manager, so you should do the same. Keep it strictly professional, try to forget the past and listen, if your new boss has constructive criticism for you. Don't just block it with: "yeah, he just doesn't like me".
For the time being, grant the new manager a ...
Short answer is that you don't. There are old sayings:
"Don't dip your pen in the company ink"
"Don't fish off the company pier"
While the getting's good in such a relationship, if it goes bad, you have to see that person every day. There's a high likelihood of HR intervening in your life, in a bad way.
Don't do it.
Establish a time frame for exclusive use of the single supplier and re-evaluate at the end of the period.
This is extremely common. Companies give better rates when they know they don't have to compete for volume.