Think that's the same with most. Maybe even less.
Yes.
Beauty of FreeView tuners is they all have an aerial in and out. Unlike most FM or DAB receivers. And most will already have a decent TV aerial - and usually fed to more than one room.
I've distributed all 5 circuits round the house using cheap telephone cable. Then pick up the wanted one - via a switch - to a local amp and speakers. Lets you adjust volume and say tone controls for those speakers easily. Unlike a 100v line system.
It's not going to cost pennies, but once done and done right lasts pretty well for ever. Same as installing adequate sockets at re-wire time rather than plodding along with extension leads.