I vaguely recall your earlier thread where you wouldn't state where you were from ("Country A, B, or C") and asked similar information. So, it looks like you came here finally as a tourist and are waiting for a lawyer to answer visa-related questions.
Is there any reason you couldn't have asked him this one, too? As a tourist from whatever the hell country you are from, you may
or may not be allowed to extend your tourist stay. (That's what you appear to have incorrectly stated above in 1) applying for additional short-term visas (business or sightseeing).)
If you don't have a visa now, how can you ask for additional ones?
You want an extension of stay for your current non-visa stay. Ok. What country are you from?
In some cases, you can get it if you have a valid reason and can prove you have the funds to support yourself during that time. That's about as specific as I can get with the dearth of information you have provided.
May I ask which methods are the easiest and shortest and most direct methods to extend my stays in Japan?
If you're here as a tourist, I've just answered the best I can. If you're here with another method, please say so, and please say how long you've already been here.
You seem to want something that lets you stay almost indefinitely until your lawyer figures out how to get you that business visa to run a branch office (representative office) for the company back home where you are employed. I don't think you're going to have much luck there. You'll just have to deal with the normal route of potential extensions that everybody else suffers.
As for your questions about the immigration offices in Tokyo, I'm sorry, but I don't live down there and don't know them. Perhaps take a friend who speaks the language would help, or go at a time when they are not so busy.