The same is true (except for size) at more or less regional/domestic only airports, English is not necessarily spoken by most staff and signage may not be in English, at all.

Like others have said, trains and the stations do have everything in English and Japanese, especially in Kyoto, Osaka, and Tokyo: it's just a lot of text and you may need to take your time to slowly find and read the English text.

Two suitcases on the subway from Shinagawa may be tough because it can be cramped, but then ther is the monorail as well. Though if you avoid rush hour it won't be too bad.