Here, I tried to centralize the main questions repeatedly asked in the groups and forums.
No!
You can begin home brewing without one (that is how I started to brew). I went to one of the specialised home brew shops, I told him I am interested in starting to home brew and want to try to brew 2 litters and see. The shop owner said that brewing 2 litter is the same as 10 litters, so I better do 10 and sold me a basic home brew kit with a step by step instruction on what to do. You can of course read some books (specially the 'How to brew' by Palmer) and they will give you a more general and special views on the home brew aspects that I cannot cover here as I am trying to keep it as simple as possible.
This question is a hard one. I used to have half day for brewing and few hours to bottling but that is not including cleaning, prep of the equipment. The time is depending on your equipment and the method you choose, for example if you choose no chill, you need to add a night to it but during that time you can do other things not related to the brewing. When you begin to brew make sure you have all day clear for it and do not rush things. Cleaning and sterilizing your equipment will take most of it from beginner to pro and commercial.
There are several ways to achieve that. I wont go into pros and cons of each system but I do want you to, at least, know they are out there:
1. No Chill Sealing the wort in a clean and sterilized container and making sure no air can go in and just let it cool down on its own.
2. Cold\Ice bucket Using some sort of container you deep the hot wort (in its own pot) in a cold\ice water and do not forget to refresh the cold\ice water. I used this system in the beginning as I did not have any other way to do it at the time as it does not need special equipment. I used the sink (sealed the drainage of course).
3. Deep Chiller A copper pipe (usually) with a cold water flowing though it.
4. Counterflow cooling A metal container that allow the hot liquid to flow on one direction while a cold water is flowing the other way. It is consider the fastest way to cool down but remember it is more pipes and connectors and container that can be contaminate.
Each system has its own pros and cons and some needs special equipment like pumps. Each is better? for the moment, the one you have the equipment for and it is working for you.
No.
A normal size apartment will do great. It is all comes to question on what equipment do you have and how much space it required to store but you really dont need a warehouse for it.
Internet, home brew forums, home brew groups in facebook and from time to time a commercial brewery publishing a small notebook with recipes. Most of my base recipe comes from Beersmith recipes