Too many questions for me to keep track of right now.
Yes, slots are one of the more obscure parts of UML in my mind. I've seen them used more with SysML and related UML extensions. They are the containers for actual values on an instance. Not sure how to better explain what's going on with that. When you model a type, you define the properties that it contains. When you create an instance of that type, those properties become containers for actual values. That's what a slot is. Ports notation for slots is just because Ports are a specialized kind of Property, and any property would be a slot on the instance. It's most natural to keep the existing notation.
13.5 (and even 14) may not show it, but the full text notation for a slot, as displayed by the version I'm using, is: <slot-name> / <defining-feature-name> : <type-name>
Oh, and EA makes the link from slot to property in PDATA/MiscData. The link is not by name.
As for re-use elements, they are used when a property is displaying the properties of its type. They are the same object as far as UML is concerned, but they kind of have a different parent, they need different relationships at times, more than one can be shown on a diagram at the same time. Having a separate t_object record for them is just a way to make all of those special behaviors work. Where possible EA does its best to allow you to see them as the same element.
I hope that answers most, if not all, of your questions.