Do you just pick a random spot to sleep in the open?

Sort of. There a many places to sleep, some of which are dark. The Infrared or Oxygen rooms are options, as is this sort of nap room upstairs. It has recliners that are laid out flat for sleeping. It's also kept pretty warm so you don't need a blanket.

Some places do close overnight, all of the rooms have been labeled. At about 1:15 am an annoying alarm goes off because after 2:00 am there is an extra $10 fee for staying over night. I have fallen asleep in the oxygen room and the red light room, there is a relaxation area in the tv/game room but I couldn't get comfortable there and that area fills up fast. The place starts "waking up" around 9:00 am.

Basically yes, although there is a lot of seating space. Also, people tend to sleep in the movie theatre area because it's dark and conversation is discouraged

You can nap in any of the overstuffed armchairs upstairs, one of the stalls in the oxygen or ionization rooms or curl up on one of the couches in the main area

Pretty much. Just be upstairs in the quiet area and nobody will bother you (unless you're a big snorer).

No, there are comfortable chaise lounges and flatbed lounges In designated quiet where you can nap.

Yes

They are huge chairs that lay flat in the relaxation room upstairs. There's a few spots that are very relaxing and you can easily fall asleep.

upstairs is dedicated space for rest but you can sleep downstairs olso if you feel comfy

There are different therapy rooms you can go into where you lay down. they have couches in the main area of the co-ed section where you can sit and read etc. Or, on the second floor they have a meditation area with reclined lounges you can sleep on.

Yes. There is one room that has a women only side. One large room has recliners that are more comfortable than the other options