It seems that only Tokyo Metro has bothered to make their rail system more accessible to foreigners, with the rebranding exercise and the much more user friendly map with each station given a dedicated alphanumeric symbol...
Will there eventually be a map showing all lines and stations run by all companies in the city? Will all maps finally be readable to the non japanese visitors?
JR East has made efforts around central Tokyo to be pretty foreigner friendly. But not even Tokyo Metro has been able to allow foreigners to buy transfer tickets yet (these are tickets that work on more than one service provider for a one-ticket trip, rather than paying in two separate instances). Those tickets require an ability to read kanji for the name of the service provider, the name of the station you want to get to, and the name of the station you plan to transfer at. There are also many warnings that are not translated, for example, at some transfer stations you need to leave the fair-paid area and re-enter, and there is a special turnstyle for this (it is coloured orange, it is quite clear to see), but the information telling you to use the special turnstyle is only provided in Japanese (and usually station staff don't speak english should you use the wrong turnstyle).
Don't expect any breakthroughs in foreigner friendly maps outside of the Tokyo Rail Map publication, which is not publicly posted information (it sells for about 700 yen). While I have a usable profiency in Japanese, I was using the Tokyo Rail Map in addition to Japanese ones (the Japanese ones were for border checks). Japan's population is 98% (or more) native, there are not many foreigners. True, this number changes in Tokyo, where there are many more foreigners, but it is still not a large dent. The private railways especially will not consider the funds justified in making their service foreigner friendly. They're preoccupied with making their systems accessible to persons with disabilities, a grossly expensive operation taking many years. JR, Tokyo Metro, and Toei Subways are the only ones that will continue to try and make life easier for foreigners.
Anyways, since the issue of the number of stations in Tokyo proper is tackled, what about the number of stations in a given area? Take your time... Does Tokyo's metro network connect to like any metro network of another city? If it does oh boy that would make counting impossible. At least if it does not, we can hope for a number for the largest cluster of stations in a given region (Still more or less in Tokyo).
By area, do you mean by ward/city within Tokyo? I can do that (many stations straddle the border though). Most Tokyo Metro and Toei lines run through service on other lines. Some lines combine to such an extant as to allow you to board a train deep in the suburbs on one end of Tokyo, pass through Tokyo, and get off well into the suburbs on the opposite side of Tokyo on a single train. Here is a list for you:
Ginza Line, Marunouchi Line - No through service (due to use of third-rail technology)
Hibiya Line - Through service on Tobu Isesaki line to Tobu Animal Park. Through service on Tokyuu Toyoko line to Kikuna (on special occasion, through service has been extended before from Hibiya Line Kita-Senjuu terminus to Minatomirai line Motomachi-Chuukagai terminus via Tokyuu Toyoko line Yokohama terminus). No
through service from Tokyuu to Tobu via Hibiya.
Chiyoda Line - Through service on Odakyuu main line to Hon-Atsugi. Through service on Odakyuu Tama branch line service (entire line through service). Through service branching off of Ayase station (Chiyoda terminus is North-Ayase station) on the JR Joban line. No
through service from JR to Odakyuu via Chiyoda.
Yurakucho Line - Through service on Seibu Ikebukuro Line branching off shortly after Ikebukuro station (via Seibu Yurakucho line). Through service merges with Tobu Tojo line at Wakoshi station.
Hanzomon line - Through service on Tokyu Denentoshi line (entire line), and Tobu Isesaki line, branching off at Tobu Animal Park and continuing on the Tobu Nikko line to Minami-Kurishashi. Through service is
provided from Tokyu to Tobu via Hanzomon.
Tozai Line - Toyo Line through service. Limited through service on JR Chuo-Sobu Local line.
Namboku Line - Through on Tokyu Meguro line (entire line) and Saitama Railway line (entire line).
There are various levels of express on many lines.