(1) either 'burst' or 'bursted' is acceptable as past/past participle. (2) it is a possible but not usual verb with person as agent and fireworks as object. 'We set off a lot of firecrackers last night' is what I would have said.
(3) Now, you want other verbs of the AAA and pattern? There are many:
"bursted" is possibly colloquial but is not formally accepted, as far as I know. "burst" is the past simple and the past participle. As in "Yesterday I burst several balloons" and "In my life, I have burst many balloons". In my opinion, "bursted" is a neologism that should not be taught. Like "quitted" or "setted". Or "hitted" or "letted". There is a tendency to regularize verbs, espec
That was my first reaction too, but have a look at [url="http://www.onelook.com/?w=bursted&ls=a"]ONE LOOK[/url]. A little research usually pays off-- it's an alternative form in AmE.
I do not use 'bursted'. However, I do use my dictionary when I am unsure of what I will write here. Webster's Collegiate lists 'bursted' as a secondary variant, which they define as 'standard usage and may be used according to personal inclination'.
That is what I based my comment on. Take it or leave it.