The expenses thing is bolloxs and if the training is compulsory then they'll have to pay your expenses to get there.
It could be that they have some other expense policy add on to cover those coming from a distance?
Doesn't make sense that they treat you so well at interview and put you off training in this way upon employment...
I'm sure a chat will clarify that travel is paid. Start from an assumptive stand point though, my avice from experience.
The room sharing is standard in many companies including my own and I think fair tbh. If you really want the privacy, pay for it.
So, reasonable and unreasonable.