Search this forum, and maybe the general freshwater for "tank volume" or "tank measurements". There's a calculator that will tell you the volume of a tank for the measurements you have. Or, you could do this the low-tech way. Get a gallon milk jug, or whatever the Japanese sell in some volume, and fill up the tank.
I love airstone, I use them in my GF tanks, so you should use yours if you like the look. If you don't, then don't use it. Space is at a premium in your tank, since it is so small, so I would avoid the box filter. However, if it is a money thing, then use it. Although not in vogue now (we do have better filters) lots of people kept lots of fish successfully in the 60s and 70s with box filters.
Small tanks mean small amounts of fish. I've always thought that more of one species of fish looks better than a couple of these, a couple of those. Since you mentioned a siamese, why not a pair of these for the tank. The females are quite subtle themselves and beautiful in their own right. They seem to prefer smoother waters, so I wouldn't do the airstone and the box filter together with them.
As for heaters, I recommend Ebo Jaegers. If you can't find them in Japan, try on-line at
www.BigAlsonline.com. As for hoods, smaller tanks seem to be more easily found with incandescent bulbs; avoid them. Try to find flourescent bulbs instead, but this may be a tall order.
Val