In Cleric table there is only +1 shooting dice (short). Is it correct?
Level 5 in Daemon Hunter +1 Shooting dice (long). It may be better +1 Shooting dice (short).
Level 9 in fighter table is not clear, short or long?
PD: sorry for my bad english
Again this is unofficial I would say
Cleric keeps Shooting Die (Short)X at level 8 as an option. Several Races also have short dice on their lists so you can use it with the right race to get up to a 3 dice attack which is not useless if taken once on the race advancement and once on the profession advancement and you can get a magic item boost or something. I do not think it would be common as you need your advancement for spells but maybe for fun.
Demon Hunter Level 5 stays Long currently. I am just trying to make the shooting advancement rules work at so maybe you want short and long dice. Would not be surprised me if it changes.
Fighter I would guess it is Long. That gives him 3 Shooting Dice (Long)X in his table compared to 4 Shooting Dice (short)X for the thief but he also starts with 1 more die.