indoor rabbits!

So I'll keep my question simply this time, in hope of an answer!

Is it necessary to have a cage for an indoor rabbit (if room is properly bunny-proofed?)
How can I tempt my Henry to sleep in a box/nest if he won't sleep in the cage?
Is there a limit to how long I should let Henry out? ppl at home let him out when I'm not home (possibly all day). When I come home I let him out as long as I'm awake and indoors.
Henry's a serial licker: I know they say it's affection but is it possible that he has psychological (longings?) or deficiency? He licks our feet, clothes - everything... all the time!

Not necessary to have a cage.

No limit to how long he can be out.

Mine are free range all the time with no cage, not even beds, they don't want them. They are litter trained.
- Mine sleep under the dining table or under our bed most of the time. I got them posh beds and they ignore them.

In an ideal situation he would need a friend, especially if you are out a lot, my bunny Nigel has improved 100% since I got Gladys for company.
Licking and grooming is a sign of affection though. I hope this helps.

Bunnie has a 42" dog crate in front room just so she's got a place of her own she can go to