Depends on the box. Some have two tuners. You should know whether yours has two tuners as it will say on the side of the box. A majority of boxes available at the moment do not have two tuners.
Yes it's true - a fact MANY don't realise. Come the day of the analogue switch off - unless you have a two tuner box as stated, you will only be able to watch/record one channel at the same time.
Its really dependant on where you plug your freeview box into. Ours goes into the av1 port on the back of the recorder, but if we'd used av2 we'd need to record from that input instead.