Lori is to be thanked for the Dawn suggestion. I don't know if she learned this through her life as a nurse, or her life as a mom, but either way it's a great idea.
I never received an Aftercare Kit from Cochlear, but I have heard of them. They were developed after I got my Divino and since my BP100 was an upgrade, I didn't get one then. Personally I think they heard of Lori's and my Official BAHA Recovery Kits and were afraid of the potential competition
I have a few blue "toothbrushes" that say Cochlear, two safety lines (look like fishing line), a jar of drying beads, and some spare batteries that came with my processors. You'll probably get similar items when you get your processor. I don't have a battery tester, but the BP100 beeps twice when your battery has an hour of power left.
Some items should be ordered through Cochlear, but truthfully some can definitely be replaced by things you can find at your local Walmart - and probably for less money. For example, the Cochlear "toothbrush" can easily be replaced by a child's soft toothbrush. I've heard of people using baby wipes to clean their abutment. Batteries can be purchased online, but I just purchase mine (Duracell, size 13) at Walmart or Walgreens.
Necessary is a matter of opinion. As I said earlier, I don't often use my brushes, I've never used my safety line (but I've found out that lots of people do), I've never used my drying beads, but that's a big no-no my friends at Cochlear tell me.
Congratulations on moving out of the newbie category!