Hi Jeff,
First off, I hope you don't mind, but I found your original post in our MethodAPI section, however it belongs in this section, "Method General Q&A", just for future reference.
Using the Method stock screens, you would only be able to assign a Work Order to one person. This might be possible to have it assigned to multiple users, however this would likely take a lot of customization to get it working and off-hand I am not too sure how it could be done. If this is a must for you, I would suggest you contacting a Method Consultant, they might be able to set something like this up for you, I provided a link here, for more information about the Method Consulting Services.
In regards to your goal to receive an email confirmation when someone else closes out an a Work Order, again this would be possible with a bit of customization. The good news for this one is, it really shouldn't be too difficult to do, there are a couple of different ways you could do this, I will give you some quick tips on one of them.
You should be able to add an action on your WorkOrderList screen (because I don't know your complete process, I am not sure the best place to put this), you could probably add an action to the existing Button on this screen for Activities->Create Invoice... or you could use the "save" button on this screen (this would only work if you aren't doing more work on the Work Order after saving it). There is an action that you can add called "Send Email", you can hardcode your email in here, so everytime this button is pushed, it will automatically send you an email letting you know.
You also asked about viewing all Work Orders from your WorkOrderList screen in Method. If you look at the top of the Work Order List grid, you will see a dropdown field with the label "Filter by View", the default is to only show "my occurences". If you want to view all Work Orders you have in your Company, simply change this "Filter by View" to "All Occurences", this should do the trick.
-Ben