'Ello, newbie here.
I’m not too familiar with unanchored parts. I just know you can push 'em around when they are unanchored. Anyway, the problem I’ve got here is that unanchored parts act anchored if, in studio, I leave them touching another part. For them to actually act unanchored, I have to leave ‘em floatin’ midair. Is this something that’s suppose to happen?..
Also, anything else about unanchored parts that might be helpful.
Do the parts have studs and the inset things on the bottom?
If two parts are unanchored and touching on those two surfaces, welds will automatically be created between the parts when the game runs.
I think the fix would be to set the top and bottom surfaces on each part to Smooth.
As @EmeraldSlash stated, this is most likely to do with Studs and Inlets causing Welds.
It could also be to do with how you’re handling Network Ownership
This is the Internal Process of how parts are handled by the Physics Engine and who controls it
If you’re far away from the object, it might not update physics-wise until you get your character closer to it or force some sort of Physics Recalculation
In total, I’d recommend uploading the group of parts to a Place File and uploading it here for us to diagnose the specific issue for you 
As EmeraldSlash mentioned the Parts may have Studs and Inlets.
When you use the Insert menu to put Parts in your game they used to start out Unanchored with studs on top and inlets on the bottom.
In the recent versions of Studio they have been changed to Unanchored with Smooth surfaces on all 6 sides.
If you started with an older version of Studio, or have a ‘build kit’ that you just copy the Parts from, check to see if the Parts have studs/inlets or smooth sides.
You can select a whole list of Parts in your Explorer window by clicking the first item, then holding Shift and clicking the last item in the list. All the selected items will be highlighted blue and you can then go into the Properties window and change all the sides to smooth if you want to do it a bit quicker.
How might I do that uploading stuff?
Edit: Nevermind. Seems I’ve fixed my unanchored parts issue. Had to test play the game while the PSGPhysicsSolver was disabled, then reenable it either during or after the test play.
Awesome! You should mark that post with a solution for a quick-find of people who come here in the future 
For reference, to upload, click “Edit Post” and then navigate to “Upload” in the middle of the nav-bar, next to hyperlink, block quote and code block.