I am Dawn1966....forgot to hide my uuser name last time.
No I do not think they would take up as much room as a Norwalk, as I think they are floor standing.
I think the press would be essential, as the pulp; and there would be lots of it with carrots and apples, would be hard to drain without one and much of the juice would be lost, also with no pulp in her stommach to digest your Mum will be able to drink more of the juice.
If you contact the group and tell them of your situation they may have information on used or second hand equipment. Ebay may also be an option, as many things sold are second hand, but you have to pay for postage, so it would have to be at a Uk location to keep the postage down depending on the total price.