the kanji for beauty salon are 美容院. The three kanji cause the word to have three syllables.
The kanji for hospital are 病院. The two kanji cause the word to have two syllables.
Well, this is not always correct since the reading of a single kanji is not always a single syllable.
e.g.
美作 みまさか: 2 kanji, 4 kana, 4 syllables, 4 morae
病 やまい: 1 kanji, 3 kana, 3 syllables, 3 morae
学院 がくいん: 2 kanji, 4 kana, 3 syllables, 4 morae
Again, mora is more important than syllable in Japanese phonology.
Most dialects of Japanese, including the standard, use morae, known in Japanese as haku (拍) or mōra (モーラ), rather than syllables, as the basis of the sound system. Writing Japanese in kana (hiragana and katakana) is said by those scholars who use the term mora to demonstrate a moraic system of writing.
The number of kana is usually the same as the number of mora, including special mora like 促音 (geminate consonant), i.e., small っ, 撥音(nasal sound), i.e., ん or 長音 (long vowel). The only exception is 拗音(contracted sound), i.e., small ゃ, ゅ, ょ, and ァ, ィ, ゥ, ェ, ォ mostly for katakana loan words, as nice gaijin-san wrote. These small kana makes a single mora as a pair with a kana preceding it.
Please check example in my previous post again.
促音(geminate consonant)
きって(切手):
3 kana, 2 syllables,
3 morae
撥音(nasal sound)
ほん(本):
2 kana, 1 syllable,
2 morae
長音(long vowel)
そう(僧):
2 kana, 1 syllable,
2 morae
As you can see, the number of kana and the number of mora are the same.
ちゃ(茶)is "2 kana, 1 mora" because there is one small ゃ in it. The same goes with き
ょうと (4 kana, 3 morae) and し
ゅっか (4 kana, 3 morae). し
ゅんかし
ゅうとう is "9 kana, 7 morae" because there are two small ゅ in it.
Furthermore, long vowels and short vowels are strictly distinguished in Japanese language. This is important especially for native English speakers who usually don't much care about the length of sound when pronouncing words.
e.g.
そこ soko(底)
bottom: 1 kanji,
2 kana,
2 morae
そうこ sōko(倉庫)
warehouse: 2 kanji,
3 kana,
3 morae
そこう sokō(素行)
behavior: 2 kanji,
3 kana,
3 morae
そうこう sōkō(走行)
running: 2 kanji,
4 kana,
4 morae
These words are totally different from each other, but they are all 2 syllables. This is another example where mora is more useful than syllable in Japanese.
にっせい; Second-generation Japanese (American)
Probably you are confusing the two words にっ
けい(日系) and にせい(二世). While the former means "Japanese descendent" as in 日系アメリカ人
Japanese-American or 日系ブラジル人
Japanese-Brazilian, the latter is "second generation" or "the second" as in エリザベス二世
Elizabeth II.
This is a bit off-topic, but this にっ is the euphonic change of にち. This change occurs before k, s, t and h/f, which changes to "p" because of rendaku.
e.g.
日記: にっき(にち+き
ki)
日誌: にっし(にち+し
shi)
日当: にっとう(にち+とう
tō)
日報: にっぽう(にち+ほう
hō)
cf.
日欧: にちおう (not にっおう)
日南: にちなん
日満: にちまん
日曜: にちよう
日輪: にちりん
日銀: にちぎん
日弁連: にちべんれん
This is the same reason why the -te form and past form of つ ending verbs change to って and った, respectively. て and た are "t".
e.g.
勝つ: 勝ちて --> 勝って, 勝ちた --> 勝った
打つ: 打ちて --> 打って, 打ちた --> 打った
勝ちます doesn't change to 勝っます because ま is "m", not k, s, t or h/f.