I'm saying find a compatible AC power adapter that's approved by one of those safety associations, and it's better if it uses a 3-wire AC power cord. I mentioned Dell only because I happened to have one of their AC adapters, and it worked with my Toshiba. As for the importance of a 3-wire cord, it should protect better against surges, and a long time ago Toshiba told people to solve a problem with their model A215 Satellites crashing from AC line surges/noise by switching to a different brand power supply with 3-wire cord.
Don't buy a replacement battery unless you know it's made from high quality lithium cells and has the proper temperature sensor. By having your old battery rebuilt, you can be pretty sure you'll end up with something that meets those recommendations, but still ask what brand cells will be used. You want something like Samsung, Varta, Panasonic, Sony, or Sanyo. And do replace all the cells, and make sure each one is the same brand so they'll charge up and discharge more evenly, won't cause some cells to carry more of the load or go into reverse polarity if discharged too much, and won't overcharge compared to other cells.
The mainstream electronic parts suppliers, i.e., authorized distributors, are the best sources of cells and include companies like Digi-Key, Avnet, MCM, and Newark, but they're pricey.