OK, some of the other points/questions in your post:
"I recently got a little coaching and was advised to explicitly activate things. He also suggested that I not use linked components, which I'm not too sure about but I can see that it prevents problems."
I am OK with half of that coaching. Regarding components, there are two workflows: internal components, and external (linked) component. Both are valuable, and have different advantages. As long as you are aware of those differences, I would not recommend avoiding external components. Just realize that there are limitations: You cannot, for example, drill a hole through an external component from the top level (unless you edit in place).
"some of my components cannot be activated. The ones I've noticed have links"
Correct. That is one of the differences. What "activation" does in a local component, really, is dictate ownership of new things like sketches and work geometry. Ownership in external components is dictated by those designs residing in a separate file. So, activation of an external component would be meaningless. The equivalent to activation for an external component is either "open", which opens that design in a new tab, or "edit in place", which opens the external design, but in the context of the parent assembly. Ownership of new object is determined by editing that other document.
"On my system, Move has Components as the default. The part discussed above cannot be selected when Move is set to Bodies."
I think if you have done a Move Components in a session, then, yes, Move will remember the last choice and use that for the next invocation. But, if you closed Fusion and re-start it, it will default back to Body. Also, if you are choosing Move from a context menu, it will set the type to the type of the object selected. So, if you right click on a body, and choose Move, it will be set to Bodies. If you right click a component, it will be set to Component. Finally, referring back to the internal vs external component discussion. You cannot do Move Body on an external component. Body move is defined to be a document-modifying operation (like adding a new sketch or extrude), so you can only do Body Move if you are editing the external component in a separate tab, or Edit in Place.
"But honestly, I'm not sure whether this thing is a body or a component. When I find it in the browser, it's icon is 3 stacked cubes, and the link icon. It contains 1 component and that contains 1 body. If I hide it from the browser, it disappears."
A couple of things packed in these sentences. First, it is important to understand Body vs Component, so being able to tell the difference is important. Fusion does not have a different name for a "part" vs an "assembly". Both are "components". If a component has one or more child components, it gets that "stacked cubes" icon, otherwise it gets just a cube icon. Bodies always have the cylinder icon:

and yes, at both the component and body level, Fusion supports visibility override from the parent component. So, even for external components, you can turn off a body or the whole component, without editing the referenced design. This visibility setting is stored in the parent design, so does not affect the referenced design
Hope this helps
Jeff Strater
Engineering Director