Welcome to the house, Angry.Felix.
Good questions [righton] , let's seee....
1. Simply, a vector image or object is resolution independent, you can make it in any size you want by scaling it and you don't lose visual content. Photoshop uses bitmap graphics which are fixed-resolution. Image focus is compromised whenever you increase or decrease the size of an image or object. Ilustrator, Corel Draw, Autocad, 3dMax - these are apps that use vector line imaging. I use Corel or Illustrator in creating complex shapes or text layouts and exported directly or as an .AI to PS for postwork.
Check out the March Project Thingy in Gary Bouton's Area.
2. I can't say the tools are duplicated but more of choices of how the palletes and tools can be displayed in the workspace. Imagine working on a large size image wherein you need certain tools. You can modify the preset contents of the pallete to display what you usually use.
And yes, there can or are multiple ways of doing the same thing.
3. If you mean the pallete dockers on the menu, I don't think so. You can stretch the palletes any way you want by hovering your pointer at the edge which turns into a double head arrow, click and drag.
You don't have to show all the pallettes. Close the ones you wont normally use. and you can summon them out with certain Fkeys ( I Don't remember the hotkeys at the moment

).
4. The pen tool is one of the most useful tools in PS. Learn to use them. If youv'e used certain vector apps before like Corel, you'll get the general idea. It's a matter of knowing where and what to click as well as which way to push or pull.
BTW, the PS pen tools act like vector tools with vector outputs (well almost I think).
Hope this helps. As a rule here in the forum - Don't shy away from asking questions. ASK AND YOU SHALL RECEIVE MANY, MANY ANSWERS.
Enjoy your time here.
vee