Yes - DropBox is an excellent solution, as also is SugarSync which I tend to prefer though I do use both for backup on different Macs. With DropBox you will have to place the folder in the special DropBox folder: with SugarSync you can keep it anywhere and nominated it to be synced. You also get more storage at the free level with SugarSync. (I have no connection with either firm.)
Yes - sending a file to any server or to an external hard disk always retains the original.