NOT A SNUG FIT from top to bottom. You need an expansion gap at the bottom or top plate. Basement floors can move (especially a 2" floor if you're correct).

You can find better articles, but this is the first one I could pull up.

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As far as fastening, PL is fine. In fact if you ever try to remove it, you'll probably split the wood before the adhesive would ever let go. I prefer tapcons because I've been known to put a plate or two in the wrong place. :) Tapcons let me "adjust".