1a) volunteer + to-infintive
1b) The adverb uneccessarily could go after to;i.e., volunteer to uneccessarily claim, but to some writers that would make it ungrammatical as it splits the to-infinitive.
2) The adverb unneccessarily modifies the verb volunteer, not claim
and the preposition without modifies justification, meaning unjustified. There isn't a double negative there.
Having said that, in looking at the entire sentence, I can't seem to make sense of the text question or, for that matter, its answer.
Student or Learner