MySql: is it possible to 'SUM IF' or to 'COUNT IF'?

You can also use SUM + IF which is shorter than SUM + CASE:

SELECT
    count(id)
    , SUM(IF(kind=1, 1, 0)) AS countKindOne
    , SUM(CASE WHEN kind=2 THEN 1 ELSE 0 END) AS countKindTwo

you want something like:

SELECT count(id), SUM(hour) as totHour, SUM(kind=1) as countKindOne;

Note that your second example was close, but the IF() function always takes three arguments, so it would have had to be COUNT(IF(kind=1,1,NULL)). I prefer the SUM() syntax shown above because it's concise.

You can use a CASE statement:

SELECT count(id), 
    SUM(hour) as totHour, 
    SUM(case when kind = 1 then 1 else 0 end) as countKindOne