Hi phelix02, some good questions you have asked, I will do what I can to answer.
1) You do not necessarily need ID unless you plan to pay for things with your credit card which is the best way to pay when travelling as a general rule. See my
MONEY MATTERS SECTION for more.
On the other hand, it is alway good to have some form of ID on you at all times. The original passport can be left at the hotel/apartment/hostel but bring a photocopy of it with you.
2)

Carry as little cash as possible and if you keep anything in your wallrt (cash, credit cards, ID, etc...), keep your wallet in your front pocket and NEVER in your back one.
As I said, some form of ID should be carried around but no need to have all your important docs with you at all times.
Try not to get too paranoid, this info is here to help and not to hinder you from having a great time. If you are paranoid you will have a horrible time here. Also, I suppose if you are over protective of your things, you are more likely to slip up and make a mistake so just USE COMMON SENSE.
The chain wallet is a good idea as is carrying it in your front pocket

but the chain should also be hidden or it will scream "wallet".
When I go out, I carry a wallet with a bit of cash and my cards in my front pocket. The tighter the pocket the better but it is still VERY hard for any pickpocket to get something out of a front pant pocket no matter how tight or loose it is
Just yesterday I met a family here to deliver a rental cellphone to them and they felt the same paranoia as you are experiencing due to all the sites they saw and posts they read. The were so afraid of losing their credit card to a thief. I calmed them a bit by telling them that they should be calm and if they have to choose between not having their credit cards stolen and having a good time here in Spain for 2 weeks, they should choose the good time. Credit cards can be replaced but a miserable time on their 2 week vacation here would stick in theri minds forever.
I hope I have made myself clear.
Do not let fear of being "picked" ruin your experience here.
Saludos,
jer...