Can Sharpness and Smite share a sword?
No. Both sit in the same exclusive group, together with Bane of Arthropods, Density and Breach. Trying to apply the second costs 1 level and the first stays as it was.
Does Sweeping Edge work on an axe or spear?
In the Java 26.1 data, Sweeping Edge only accepts swords. Axes take Sharpness, Smite and Bane of Arthropods, and spears have their own Lunge.
What is the maximum level of each?
Sharpness V, Looting III, Sweeping Edge III, Fire Aspect II, Knockback II, Unbreaking III and Mending I. Books above those levels do not exist in Survival.
Are Knockback and Fire Aspect worth it?
That is taste. By price, Knockback II is one of the cheapest books on the list (2 levels, like Mending) and Fire Aspect II costs 4. They weigh more on the anvil order than on your wallet: with both, one by one stops being feasible.