Japanese computers were specifically made to handle kanji and had higher resolutions than contemporary western computers, so there wasn't really any issue with kanji support. The higher resolution and larger color counts led to something known as CG (computer graphics) back then (now just called イラスト / illustrations since CG now usually refers to 3D graphics). It ranged from 8 color CG in the late 80s, to 16 and 256 color CG in the 90s and near the turn of the century 16 million colors were introduced.
Sharing CG on BBSs was really popular during the 90s and a lot of prominent BBSs even had their own custom advertisement CG. 16 color art dominated since the PC-98 was the most popular system in Japan during that era and it lend itself well to the anime art style. They also shared FM and midi music on BBSs, but CG was more popular. Other than that they used BBSs similarly to the west and shared files and talked about various things.
With the advent of the Internet, many CG artists created their own websites for their CG and a forum called NiftyServe gained a lot of popularity and BBSs started to lose their significance. A lot of CG artists had a really hard time to transition from 16 colors to 16 million colors and quit, but some artists like Wakachan and Goto-P are still active to this day.
As for what software they used, I can't give much information as it doesn't interest me much, but they did use their own software specific to Japanese computers. Some of it might be available in the vector.co.jp software library. The source of my information is visiting some BBS archives, a lot of CG artist and FM/midi music creator sites, plus other old Japanese sites and reading the tidbits of information they shared.
PS: Japanese BBSs had their version of newfags that wanted to get spoonfed called CG beggars.