How much can I expect to spend over 3 weeks in Japan?

With everything as minimal as possible- such as cheapest air plain tickets, cheapest motel, .. lol. lowest everything??

LOL...over 3k to 4k

Flight, board, transportation, nourishment, entertainment; you could get by with $5000.00

Hope you enjoy your trip to Japan.

1000 on average for roundtrip ticket. about 300 a week for hotel, but thats a major city.

3 weeks hrmm, Depending on where you're staying. There are a lot of cutty cheap places in Tokyo if you know your way around.

IF you want a cheap air plane ticket you have to make connections and it'll take twice as long but it's cheap. I recommend China Airway.

For hotels. Super Hotel is very acceptable. Theres many locations, check out their site. Small but cheap. But what isnt small in Japan lol.

If you're planning on traveling the country, for sure get a JR Rail pass. Only foreigners can purchase this. Soo worth it. and you can go on the Shinkansens (bullet Train) suggest going to Kyoto, it;s beautiful.

Food: Pretty much everything in the departments/ restaurants in major train stations are going to be expensive, not all but most. but worth it. Try small places inside the districts, just communication might be a problem but it's do able with simple words and gestures.
You could also survive off of 99yen stores. and convenient stores like Lawsons, Seven Eleven, and Sunkus etc.

It depends the area you want to visit.
In Japan, everything is charged, you should expect more expense than traveling to other countries. (Avoid using Shinkansen-train and Taxi).