Hi Sino,
Sorry this is a bit long-winded, but I want you to be completely clear on what is happening. That way you can get EA working for rather than against you.
The answer to your second concern - deleting in the Project View - is that here you are doing something a bit different than on a diagram.
The Project View is a list - actually the list as far as the UI is concerned - of what exists in the project. Each icon in the Project View represents the actual item in the project.
Contrast this with a diagram. Even though I can use a diagram as an easy way to enter items into the project, what's shown is only a representation of the item itself. I could later add another representation of the same item to another diagram. Each diagram could have different display settings - features might be shown on one but not the other, parameter display could be set to 'full' on one and 'type only' on the other, and so on - but the diagrams are both showing images of the same[/i[ item. Only a single instance of item itself exists within the model. This single instance is what is shown in the Project View tree.
When you delete an item from a diagram, you are by default only removing that representation of the item, but not the item itself from the model. If you were to open the other diagram, its copy of the item would still be there. And if you dragged the item from the Project View onto yet another diagram it would appear as expected.
Contrast this with deleting an item in the Project View. Here you are removing the [i[actual single instance of the item from the project. Once removed it is gone, entirely. Any diagram that had a representation of the item is out of date, and is immediately amended to remove the image of the item.
The same is true for any connector (link) that an item participates in. When a representation of an item is removed from a diagram, so too are representations of its links. When the actual item is removed from a project, all links it participated in become invalid (since one or both ends now go noplace) and they too are removed from the project. The links no longer appear on any diagram.
By default EA will warn you when you delete an item in the Project View; you have to confirm deletion. By default EA should at least ask you, when you delete a link or an item from a diagram, whether you want to delete that image of the link or item or remove it from the model.
In the case of deleting an item from a diagram it is possible to set EA to always work the same way (delete only from the diagram or remove entirely from the model). This (setting the default) is easy to do without really noticing, and thereafter you don't get asked.
Try deleting from a diagram wth control-delete (or shift-delete if that does not work) and see if you get a dialog. Pay close attention to what it says.
In the case of the Project View, I am not sure if you can turn the warning off. I keep thinking that I have seen some way to do that, but I really don't what to set that option. I'll happily live with a few extra keystrokes in order to have a safety valve. I sometimes have to delete a bunch of elements from a model. When this happens I either take the time to go through them and answer OK to each, or drag them into an empty temporary package and delete the package (and thus its contained elements).
HTH,
David