I can upgrade my Hero Nord Sword and Ancient Nord Bows, but when I make a Hero Nord Bow it does not show up as an option for upgrading on the grinding wheel. Is this a bug? Or am I missing something?

There is a mod that fixes that. It doesn't work for anyone in the vanilla game.

It's identical to a Hunting Bow in damage output though.

Legendary Nord Hero bow is fourth most damaging bow in the game, after Karliah's, Daedric and Ebony.

Thanks. I will have to look for that mod. My current character uses only Ancient/Hero Nord Armor & Weapons for RP reasons. That's why I was looking to upgrade them.

Hero Nord items? Which level you'll see them? 44 levels made me only to see honed and supplient weapons which both seems to be unable to upgrade.

You'll never see them, you make them yourself at Skyforge after completing the Companions questline.

I see. I have almost completed it with one character but I got tired with it because they are giving me repeating missions again and again instead of the last part of the Totems of Hircine quest.

If you're doing the Totems then the questline is already completed It ends with Glory of the Dead.