Your second link is for an older version of the API (1.6), don't use that. I would start with reviewing all the ESRI provided info in the Concepts section. http://help.arcgis.com/en/webapi/javascript/arcgis/help/jshelp_start.htm Just get familiar with it. Going over the samples and trying things out is incredibly helpful.
This also varies on your background, if you have done some development in another language before, which is quite helpful, but not a hard requirement.
Editors are really a personal preference. Aptana seems to be a popular choice. If you come from a .NET background, then Visual Studio might be easier. Both have plugins for intellisense if that's your thing. Notepad++/vim don't have intellisense, but I think force you to really delve deep into the docs when you need to (personal opinion). I would say try a few and use what ever helps you be more productive.
Dojo is a javascript framework, one of many, but the one that the ArcGIS JavaScript API is built on. The two are joined at the hip, so it would be quite worth the time to read up on it.
There are some Dojo books out there and they still have some good info, but since 1.7, the Dojo site is probably the number 1 resource. The docs have improved greatly since last year, it used to be a trainwreck, but today are incredibly well written.
