I've just cosplayed Schrodinger (best costume I ever did for so many reasons), so I shall help you!
1. Back in the old days when it was just the manga, quite a few people did green, since nobody knew what colour he was really supposed to be. However, since the OVA has come out, it's pretty much agreed that Schro wears some kind of horrible yellow/orange colour, although most people (myself included) go for a light khaki brown colour.
2. Again, since the OVA has come out, Schro's shorts are black, unless you're doing the manga version, in which case they are the same colour as the shirt. If you're doing manga version, the tie has a white pattern on the top, while it's red in the OVA. For socks, I bought ordinary black knee high shorts and used cotton twill tape to put the stripes on. The shoes I used were in fashion a while ago, so I found mine in a charity shop and then just put fabric around the top.
3. I made my own ears using some special 'paper' I found at the craft store (I wish I knew what it was called - it had a really weird texture) and some VERY short fur (one of my pet peeves is people who cosplay Schro and use long fur for the ears - cat ears aren't like that! Other pet peeves include doing the ears too big and at the sides of the head) then sewed them into my wig to avoid having to wear a headband, which I just think looks a bit naff.
4. The swastika is a matter of personal taste - you'd be forgiven for leaving it off. When I did Schro, I made two armbands, one with the swastika and one without. I started off wearing the swastika and told myself I'd take it off the second anyone said anything about it, but the need never arose to wear the armband without the swastika. In fact, I had alot of people compliment me on my courage to wear it. However, this could vary from con to con, so don't listen to my story. I'd rather you be prepared than just go in swastika and offend alot of people and not have a second armband to wear without the swastika. I live in the UK, and I'm assuming you're from the USA since that seems to be where most people on coscom are from, and I dont know how attitudes vary from country to country.
5. I bought the subtle fangs from vampfangs.com, and they are amazing (don't go for the natural fangs, because they just don't look ...natural). A word of advice on that - when you're moulding them to your teeth, the instructions say use a whole capsule per fang, but I find half a capsule works much better. I've also ordered red contacts from vampfangs since they were on sale recently, although I havent recieved them yet since I only ordered them a few days ago, so can't tell you anything else about quality or what they're like.
Anything else you wanna know about Schro or if you need help, get in touch! I love Schro and it was my favourite costume ever, so I'm really happy to help other Schrodingers!
(This is my costume here : http://www.cosplay.com/costume/148360/
Use it for inspiration and feel free to ask if you wanna know how I did anything on it. My costume is a weird mix of the manga and OVA versions, since there are parts about both costumes I like/dislike, so I took the best elements from both versions while leaving out the bits I didnt like.)