Well. The icon of an app is appearing on the dock. I don't want it. Right-click, then options, then remove from dock. OK. Some times later, the same app is on the dock again. How can I get rid of it for ever there... ?

If you drag an item out of the dock when the application is not running [you'll see a little animation], it should no longer show up there. However, whenever you open the application again, its icon will again appear in the dock [the icon of an active application is always in the dock] -- but when you quit the application the Dock should remember that you'd previously dragged the icon out and the icon should again vanish from the dock. Occasionally I come across an application or utility that leaves its icon there even after you quit it -- I don't know why those applications do that, but dragging the icon out again usually fixes it.