Jennie

My bunny likes to sleep in my lap. I hold her in my lap for almost 1 hour every night when I watch TV. When she sleeps her eyes are almost closed and sometimes she takes a sudden deep breath in her sleep. When she wants to return to her cage she would lick my arm and let me know.
In fact, she likes to sleep in the lap of any one in my family.  She is 3.5  years old.
Rabbits sleep more and longer as they grow older.

No, bunnies need not to be neutered/sprayed in order to be litter trained. Just give them a litter box with shavings and some hay when they are young and they will learn to use it.