Hi Konrad, as I left early I did not take part in the actual session. Great to see that you liked it.
Here some answers to your questions:
The Facilitator also reacts during Reaction Round. Most of the time I try to use it to coach the Partners on how Holacracy works based on the tension that is there.
The Policy vs Domain is often addressed on the CoP. If the Facilitator feels that a Partner might want a Domain instead of Policy then the Facilitator can use the Clarifying question round to get more insight. F.e. do you want to restrict all circle members to impact this? And then I would use Reaction Round to explain what the difference is between a Domain and a Policy. The Proposer can than change his/her Proposal based on this learning
The Facilitator may object based on current knowledge he/she has so it is possible that a Facilitator who is not having any roles in the Circle objects. I agree with you that most of the time the objections come from NVGO as the Facilitator has the role to safeguard the Process.
Hope this helps.