When killi keepers re-wet peat, it means that there are killie eggs in there and they do so to make them hatch.
You boil the peat mainly to make it sink, skim off the floating bits, drain off the water and keep it to add to your tank, and put the remaining peat into a bag and either put it in your filter or hide it in the tank somewhere.
There are many types of Oak, the difference mainly being in the leaf shape. These must have aged naturally and fallen off the tree dry before you add them to your tank, either loose (they sink after a couple of days) or in a bag. As i mentioned before, you could also put them into a large container of water and use if for waterchanges as well, just keep topping it up as you use the water.