No restrictions on lot traits, and yes, the lot has to be an EA-created one.
@Deklitch, if you use earphones, you should be able to hear. My PC doesn't have speakers, but the headphones I picked up at the grocery store work fine.
To clarify on what you can do during the rest period -- if it raises a need, and it's not specifically connected to a challenge (i.e., fishing, playing an instrument or singing, working out), then you're okay. If the need is in full green, then you have to do something else.