For the sake of Haiku or in general, how are syllables counted in Japanese?
Specifically, in the following cases, how are syllables counted?
The general method of counting in Japanese poetry is by a rhythmic unit known as the mora (morae or moras in plural). A mora is (essentially) the length of a single (full-sized) kana; so is a bit different from a syllable.
For instance:
A long vowel is counted as one syllable, but two moras. e.g. えい is a single syllable, but is two moras.
ん is counted as a single mora. 関係：かんけい is two syllables, but four moras.
Yō-on take up one mora in all, because the sound is contracted into one rhythmic unit.
Sokuon count as an extra mora. e.g. 一杯：いっぱい is two syllables, but four moras い っ ぱ い
Thus, applying those rules to your examples:
かあ : two moras
きゅ : one mora
ポッキー : four moras
ん : one mora
Hope that helps!
Note that in Japanese poetry, there is a marked avoidance of moraic ん as well as Sino-Japanese lexicon and onbin, so the question is often irrelevant as all the syllables occurring are of form CV. However, if required, きょ would be still one syllable (strictly saying, mora), while じゃく or った be two.
