It's not clear from your posts, but it seems you are saying the your iTunes does not recognize your iPhone when you plug it in. If that's so, you have bigger problems than adding or deleting songs. You have no way of synching your phone with your computer and worse no way of getting critical updates to the iPhone software.
You do not add or delete songs from the iPhone directly. You add and delete songs in one or more playlists in iTunes. You then specify, in iTunes which playlist(s) you want to sync up with the iPhone and then finally sync up the computer and iPhone. All of this hinges on iTunes recognizing your iPhone when it is attached.