I'd say no to the bow; the PHB is quite clear: "You can't use a ranged weapon as a melee weapon."
Similarly to the shield: "However, you can't use your shield hand to make attacks." I don't think I'd consider the shield to be a weapon, if it can't be used to make attacks.
Fist, I don't have an issue with. But I'd be disinclined to allow someone to point out that it refers to kicking as an improvised weapon as well, and call their greatsword-and-kick an answer to "You must be wielding two melee weapons".
-Hyp.
The counter-argument is, of course, the line: "Improvised weapons include anything you happen to pick up, from a rock to a chair."
OK, so the rules provide a little guidance.
Ranged weapon are specifically excluded, so no whacking critters over the head with a bow (although stabbing with arrows a la Legolas may still be possible), and possibly no shield bashing, at least not with a properly mounted shield (although this one I am less sure of, since shield bashing has been around as a concept for a long time and was an explicit part of the last version.)
Wait a sec....
Ah ha! Shields don't work because they weigh either 6# (light) or 15# (heavy) and the maximum weight for a one-handed improvised weapon is 5#. 6# improvised weapons are two-handed. So you can grab a shield off of a table and whack someone with it, but you have to use two hands.
But rocks and chair legs are still legal - as is a piece of wood the same size and shape as a bow, just so long as its not actually a bow (??). And, by a strict RAW unarmed is listed under "Improvised Melee Weapons", so that may still be allowed - it works for Opportunity Attacks, after all.
(Personally, I think I would have allowed (and may still allow) them to use a bow for an improvised attack, but the attack would break the bow as it's not meant for such abuse. But that, of course, could have repercussions as seen here.)
Carl
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