why are 'na konferencjach' and 'na konferencji' accepted as the same?
This is a mistake most likely. "na konferencjach" is plural and "na konferencji" is singular. This should be reported as an error.
Why 'przemawiac' is wrong..? You can 'mowic' anywhere you want but at the conference people make 'przemowy'.
Yes, that would be an even better answer, reported it.
Why is 'gadac' wrong?