1) I would definitely leave it alone for tonight, at least. Some hedgies might need 2 nights to get settled and not be overwhelmed by being taken out of the cage. It's very rare that a hedgehog will actually *come* to you
Once it's a little more social, it will probably just end up being tolerant of you picking it up.
2) That definitely looks like the aftermath of a good anoint.
3) In the beginning, you want to take things really slow and calm with your little one. There should be no swooping
I find it best if I gently wake my Mildred up either by saying her name or touching the fleece she is hiding under softly. Then I show her my hands. She usually quills up and huffs and then I slowly move my hands to her and pick her up. Some nights she decides to huff a lot and not calm down, so I take a piece of fleece, lay it over her back and tuck it under her tummy, then pick her up. Someone said that it won't hurt to pick hedgie up, but that depends on your pain tolerance and your hedgehog. I have been handling my hedgie for 5 months now and I still can't pick her up when she's in a ball because it hurts my hands. Start off using some sort of cloth (no gloves!) to pick it up and eventually either your hands will get used to the quills or she won't get so upset when you try to pick her up.
4) The best thing to do in the beginning is to either use a snuggle bag or a piece of fleece, a blanket, whatever, to hold hedgie on your lap. It will want to burrow around and hide from you and whatever light you have on. Start off letting it sleep how it wants to, whether that's all wrapped up in a blanket, or with it's head out. Eventually, introduce laying your hand down over hedgie's back. Do that for a while, then maybe start putting your hand near hedgie while it's on your lap so it can smell you and get used to your hands being near it's face. Take everything slowly, step by step, until you can work up to laying your hand directly on it's back or having it sleep on your arm, on your stomach, etc. I have read that holding hedgie by your chest can help with bonding because they can hear your heartbeat? My hedgie seems to like it.
5) You already got answers about the cage, but remember - bigger is better. A lot of people here at HHC seem to have cages that are around 6 square feet. 4 square feet is recommended, but by the time you put in bowls, the wheel, a place to hide, toys, etc, there isn't an awful lot of room left for hedgie.
6) You definitely want to invest in an igloo. The recommended size seems to be the medium size, which is around $6-$8.
Also, you should put some duct tape on your wheel over the spot where the two pieces of plastic meet. There's a groove that runs between the 2 pieces and there have been reports of issues with it. Save up for a Carolina Storm wheel! They are wonderful wheels and the guy who sells them (Larry) is great.
It's wonderful that you came here with your questions. And it's also great that you are so excited to bond with it! Just remember that hedgehogs are naturally defensive animals and it will take a lot of patience.