Hi Freddy. In answer to your first question you use the 'export' option. Once you are done with an image and want to save it you right click or go to the 'File' menu and select export. This will bring up a dialogue box with lots of options. You can specify where you want to save it, what name it should have, what size it should be and what format it should be in (i.e. RAW, DNG, TIFF, JPEG etc). Once you made your selections hit the export button at the bottom of the dialogue. This will save the image as it is at that point. You will see your export listed in the develop module under history.
You can then start working on the file again making more changes - to black and white, or higher contrast or whatever. When you are ready to go just follow the same procedure and export. The dialogue box will have kept your earlier settings. (One of the great things about LR is that there are many ways to achieve the same ends, so in this case you can also use things like the virtual copy setting and the snapshot setting, but at the moment that would only be more confusing).
In answer to your second question, LR never saves changes directly to the original photo. It creates what is called a sidecar file for each image which lists all the changes you have made while editing. When you open the image again for editing the settings from this sidecar file are applied so that you can see what the end result will be. The settings are only applied directly and the image changed when you go through the export process where you are creating a new image.
I'm not entirely sure what you are getting at in your third question but when you export an image you specify where it is to be saved. You can set up LR to automatically add certain folders to the catalogue otherwise it will not do so and you can choose whether or not to add them yourself through the import files/folders option or through the synchronise option if the folder has already imported into LR. Files are always saved to the folders you specify, they are never actually saved to the catalogue. The catalogue is just LR's way of organising and managing all the information about your images. Think of it like a traditional library - a library catalogue will have all the information about the books in the library but the books themselves are out on the shelves.
Hope this helps. LR can seem a bit overwhelming at first but it's worth keeping with it because it is (IMHO, of course) the best there is.
