I hope that someone can help me with the following. How can I make Dropbox i) stop synchronizing a particular folder, ii) erasing that folder and all its files from the web, but iii) keeping the local folder and its files in my computer?
The easiest way is to move out of Dropbox folder everything (files/folders) you want to keep on your computer but not in the cloud. 😉 When you move something out the result is exactly the same you are looking for.
If for some reason you want keep the particular folder within Dropbox folder, you can use ignore feature.