Unfortunately it is very much illegal to ride with an umbrella (I've totally done that too though... technically speaking riding on the back "seat" of someone's bicycle is also illegal, but you see it all the time in dramas/movies...), but the police can't do very much if they catch you... unless they catch you a lot... that's where you have to be careful as a foreigner... The only way around it is full out rain gear (long waterproof jacket and pants... lots of people ride bicycles or motorbikes in the rain so you can find these lots of places... not so attractive, but it mostly keeps you dry...)
Hanabi is usually mid-late July and early August... The biggest ones in Fukuoka seem to be:
1. 西日本大濠花火大会 (Nishi Nihon Ohori Hanabi Taikai) In Fukuoka City on August 1... not so big, but in the city, so lots of people show up...
2. 筑後川花火大会 (Chikugogawa Hanabi Taikai) Probably the biggest in terms of number of fireworks, in Kurume, maybe on August 5 (haven't announced the official date yet)... also apparently they've been doing it for 352 years... Japan has a long proud history of hanabi!
3. 関門海峡花火大会 (Kanmon Kaikyo Hanabi Taikai) This one is actually in the strait between Kitakyushu and Shimonoseki in Yamaguchi, it attracts more than a million people, but if you divide that between two shores its not so bad... 2nd biggest in terms of # of fireworks... It's on August 13...
Then there are tons of smaller events all over the prefecture... all (or most) of them are listed here
http://hanabi.walkerplus.com/list/fukuoka.html
if you take a train make sure you either have an IC card (prepaid card) or you buy a roundtrip when you board, or a return ticket as soon as you get there cause the train station will be mega crowded when you go back!
I'm always outside Japan during hanabi season (its for work so it can't be helped), so see lots of hanabi for me!!
And rice cookers you should be able to find in a recycle shop, but if you can't there is always Rakuten (gotta love the internet...)
http://search.rakuten.co.jp/search/mall/%E7%82%8A%E9%A3%AF%E5%99%A8+%E4%B8%80%E4%BA%BA%E6%9A%AE%E3%82%89%E3%81%97/-/
(this is the search for 炊飯器 一人暮らし... rice cooker living alone)