To prepare his daily spells, a wizard must first sleep for 8 hours. The wizard does not have to slumber for every minute of the time, but he must refrain from movement, combat, spellcasting, skill use, conversation, or any other fairly demanding physical or mental task during the rest period. If his rest is interrupted, each interruption adds 1 hour to the total amount of time he has to rest in order to clear his mind, and he must have at least 1 hour of uninterrupted rest immediately prior to preparing his spells. If the character does not need to sleep for some reason, he still must have 8 hours of restful calm before preparing any spells.
so yes, they can all do that. other spellcasters, such as divine caster, don't even need to rest at all for spells. Bards need to rest like wizards but only take 15 minutes to warm up and have spells ready.
No, you can't.
When preparing spells for the day, a wizard can leave some of these spell slots open. Later during that day, he can repeat the preparation process as often as he likes, time and circumstances permitting. During these extra sessions of preparation, the wizard can fill these unused spell slots. He cannot, however, abandon a previously prepared spell to replace it with another one or fill a slotthat is empty because he has cast a spell in the meantime.
You refresh the slots once a day, the first time you study. Then you can use each slot only once (unless you use a pearl of power or other abilities/items) until you refresh the slots again the next day.
Even divine spellcasters can only renew their spells once per day, usually at a set time, like dawn or dusk. So varied rest times make little difference to them. It's once per day, period.
I don't think they're hoping to refresh spells more than once per day, just wondering if they can refresh them with broken rest if necessary.
Hmmm, yes, probably you are right.
In the past, I have seen a few people arguing that is possible to refresh the spells multiple times in a day, so I replied too fast, without reading carefully.
Our party will be in one spot for a few days. I am looking for rules on if resting and/or sleeping in 3 to 4 hour shifts at a time 3 to 4 times per day is feasible by the rules. If this can count towards rest in order to get spells and abilities back, I'd like to see the official ruling on this.
If you've got PCs standing watch, that will reduce their rest time, and as seen above, most spellcasters require 8 hours of rest, more if it's interrupted.
The OP asks about "spells and abilities". The above answers primarily concern spells. For any abilities expressed as x times per day, there is no way to get around the 24 hour lag period.