Yep. Athserisar it should be. As it seems we don't have the word specifically in a noun form from David yet, there is a very slight chance that it's somehow off, but the derivation pattern is one of the most dependable in Dothraki.
1. All normal adjectives work as stative verbs too, there isn't really difference. Irregularity is very rare. Maybe if the adjective ended in /-e/ you might think the epenthesis were messing with the system, but with seris does not look suspect.
2. Verb nominalization is probably even more dependable. Pretty much the only concern is that the word might be reserved for some narrower meaning or some synonym might be the one that were traditionally nominalized. Unlikely.