tsunami seems a strange word to borrow when english has a perfectly good one already: tidal wave. tsu means harbour according to a dictionary i once checked. nami is wave.
the mt fuji phrase does sound very japanese.
when i was first here i noticed mountains were called "san". not knowing any japanese at all, i assumed it was the same respectful title as given to people (as in "sakezuki lusy san"). i was very disappointed to discover it was just another reading of "yama", mountain.
most kanji have more than one reading. in this case yama is the japanese reading and san the chinese one.
another time i went skiing with a friend and noticed on the car navigation the kanji for "waterless mountain". pretty pleased that i recognised the kanji i read them to him, all in chinese reading: "suimusan". of course i was wrong on all counts! it should be "mizunashiyama", which probably has a better rhythm.
so while westerners often say "fujiyama", this puzzles japanese who would only ever say "fujisan"
(which is also the name of a really nice beer from asahi!)