The are foreign friendly services, but yes the majority are Japanese only. Mostly they don't want to deal with the language barrier, and they don't think that non Japanese will keep there mouth shut as its all illegal.
That said they are yes mostly natural, but somewhat groomed, not a jungle.
Yes gaijin is technically the slang word for non Japanese. It does have a negative connotation.
But that's just the Japanese being xenophobic as per usual.
Yes size can be an issue, most can't handle it, but the majority of my punts I have had no issues. The moaning is more annoying then anything, but the foreign friendly ones tend to not sound like someone stepping on a rat.
The majority of the stuff in shinjuku and ikibukuro are run by the yakuza which is also why it's not all that friendly to non Japanese as we are less likely to put up with their shit and cower in a corner.
But the services that are mentioned are very useful if you find yourself there and yet affordable to the avg bloke.
As with all things YMMV but if you stick to the "delivery health" services you should be fine.