What constitutes a syllable? For the sake of Haiku or in general, how are syllables counted in Japanese? Specifically, in the following cases, how are syllables counted? * , long vowels - two syllables? * , addition of yō-on - still one syllable? * , addition sokuon - small tsu counts as a syllable? * ?

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. is a single syllable, but is two moras.
>
> is counted as a single mora. 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. is two syllables, but four moras

Thus, applying those rules to your examples:

> : two moras
>
> : one mora
>
> : four moras
>
> : one mora

Hope that helps!