I couldn't find detailed information due to my limited Japanese sorry.
And yes, it seems true that the fireworks takes place every saturday in December; no details for 2017 have been published yet I think, but it technically would be 30 Dec.
However, it seems that these fireworks are pretty short, e.g. 10min
Not sure if it's worth it, but if you really want to experience it, you can join a boat cruise that includes food/drinks , costing over 10,000 yen pp.
ELH- New years eve in Japan/Tokyo is not a big thing, many people line up at the big shrines before midnight to be the first to make offerings in the new year. Not so perhaps. Many bars and restaurants may hold NY parties but maybe require booking in advance (not sure about this)