Why can't I add a piece twice in an assembly?

can you show a screenshot of your feature tree?

Are you not able to add a duplicate component at all?

Are you using the Insert Components command?

or are you Ctrl+LMB click and dragging the part to duplicate it?

Or perhaps dragging the part in from another open file?

Or dragging it in from a Windows Explorer folder?

When I first started assemblies I kept getting FIXED parts with the "(f)" like <1> and <2>, when I really needed FLOATING parts like <3>.

You can RMB on the part in the FeatureTree and select Float to unfix a part.

<2> was inserted with Insert Components command. It is stuck in exactly the same position as <1>.

<3> was a Ctrl+LMB click and drag. It is free to move and rotate and all that.

There's a pin icon on top of the insert part tree. Tick it, and whatever part you've selected will come up in assembly area upon clicking mouse