What shouts does Paarthurnax teach?

Question

If I have learned all of the fire breath shouts, will Alduin teach me some other shouts or just not teach anything and be useless?

Answer 1

Looking at the elder scrolls wiki, it looks like Paarthurnax will only teach the words of power pertaining to the Fire Breath shout and none other; he will teach you the next word you need (so if you have the first he gives you the second, if you have the second he gives the third). However, it also looks like it is not possible to get all 3 words of power for Fire Breath without Paarthunax because outside him there are only two word walls (in Dustman's Cairn and Sunderstone Gorge). Here is the wiki page on Fire Breath and Throat of the World to see for yourself.

The Fire Breath page lists the locations for the words of power underneath the article picture and the Throat of the World page lists only Clear Skies and Fire Breath as rewards (and Clear Skies is from the Grey Beards).

Answer 2

Paarthurnax will only ever teach you 1 word of the Fire Breath shout.