Can you paralyze dragons

According to UESP, in order to improve an item to Legendary quality, you'll need to increase your Smithing skill to 168 (since you won't have the Smithing Perk for that armor type). Given that you also won't have any Enchanting perks, I don't think that you'll be able to find/make a set of armor and Fortify Smithing potions to get your Smithing that high.

So no, I don't think that Smithing and Enchanting skills can be entirely replaced by potions.

The only truly unique bow I know of is the Bow of the Hunt, which has a unique enchantment (+20 damage to all animals) and it can be found in Clearspring Cave

If you have the Dawnguard DLC, you can obtain Auriel's bow, which is a bow with a rather unique effect.

There is also a list on the wiki for unique bows that always appear in a particular spot in the game. Note most of them are unique due to its name only, their enchantments and looks can be duplicated.