I will try to answer some of your questions.
Discretion is down to individual councils with some being more forthcoming than others or I could say some being more aggressive than others.
To be honest I don't think council choice's come into play very much, most decisions having been pre-arranged by central government rules, with the little bit left to the council to decide on, being dictated by financial restraints.
In my position, I was granted 13 weeks discretion on medical grounds, which have now expired and I am now having to pay the bedroom tax on 1 spare room.
As my son is moving out soon, I will have to start paying for two extra bedrooms.
I have applied for discretion again on medical grounds and because I have reluctantly agreed to downsize. I am awaiting a response from that, which is taking a very long time due to a back log of paper work.
Funny that though, somehow because I stated my son would be moving out sometime in the future, for some reason they decided that meant he had already moved out and they sent me a letter telling me I was in arrears and demanded payment.
As for cost of moving, should they ever find me a place to move to, this used to be covered with an enticement payment of £1000, meant to encourage tenants to downsize in the past. Due to this bedroom tax, I am told that this pot has long since run dry in DDC and it would be up to me to pay for any move that might arise.
I have to say that DDC are doing more than some other councils but the money they have been given for discretionary payments will not last long and unless they dig deep into other funds, this situation will get worse, which believe me, many people cannot even begin to know how that feels.