Name in English of different parts and tools
We have a terminology index here that should help you with the more common names. Please feel free to suggest anything that is missing (we do try to keep adding things that are missing)

Unfortunately it doesn't currently have the things you're asking about. The part you've shown is a freewheel, and the tool is called a freewheel remover. You also need a chain whip to hold it in place while using that tool. (edit: no you don't). Note that there are several different types of freewheel removal tools because there are different types of freewheels. See this blog post, for example.



Also, modern bikes tend to use cassettes rather than freewheels. The difference is explained here by Sheldon Brown and here's a picture from his site showing the important bits: