The kana syllables are grouped by their consonant, so a direct transliteration would use the same Latin consonant for all kana in a group, e.g. "ta-ti-tu-te-to", but when it is desired to suggest the English pronunciation, like in the Hepburn transliteration, that corresponds to "ta-chi-tsu-te-to".
Before WWII, the kana spelling corresponded to a much older Japanese pronunciation, from about one thousand years ago, so there were much greater differences between spelling and pronunciation. So in my examples, what was written "yahara" was pronounced "yawara" and today it is written like it is pronounced, what was written "osahe" was pronounced "osae" and today it is written like it is pronounced, what was written "kuwatu" in kana had been earlier pronounced as "kwatsu", then the pronunciation has become "katsu" (= life) and today it is written "katu" in kana and "katsu" in Hepburn transliteration.
Even when you know some Japanese, reading any book published before WWII can be difficult, because many kanji used before have been replaced with others and the kana spellings of the old kanji can also be confusing because they are different from the modern spellings too.
You are right about the transliteration of English words into kana.
This seems unlikely. The pronunciation was tsu before WWII. But the organization of the syllabary strongly suggests that the pronunciation was once tu.
I don't know to what degree the syllable 'tu' is viewed as impossible in Japanese as opposed to merely nonexistent. (Compare Mandarin, where (as in Japanese) there is no syllable /si/, but it's not especially difficult for Mandarin speakers to pronounce /si/.) I'd be interested if you knew.
Isn't that why English words ending in -t or -d get transcribed into Japanese with a final vowel of -o rather than the -u that is used for other final consonants?