If i summoned breaker, can i use my priority 2 use his effect before my opponent chains it with traphole?

No because when Breaker is summoned you have to put the counter on it so if you were to use Priority when your Opponent uses Trap Hole, then you would only be putting a counter on it. So you cant use Priority to destroy a S/T.

Technicaly you conradicted yourself soul taker. Breaker's priority IS to put the spell counter on him. Now here's a question, is breaker's token optional? I dont really have the card in front of me right now.

The turn player has no priority whatsoever, in this scenario, because a triggered effect has been activated and forms a chain. The turn player only has priority on an empty chain.

Breaker's triggered effect to place a counter on itself is mandatory and must happen if it is normal summoned.

Not that it mattered (you might see people opting not to put the counter on and instead using priority to sac it to cannon soldier). Breaker can not use its ability to remove a counter, so I suppose thats all that needed to be said.

I believe that Breaker's effect of gaining a counter is not optional.

While it is true that I could have explained it in a different way using not so many words, it is usually better to go a little more into detail for those who might want to read this thread for an explanation. Helps to answer any questions that float around in their minds.

How about chaos sorcerer and chaos emperor dragon? can they use their effect b4 being chain by bottomless traphole?

A player has priority to use any monster with an ignition effect as long as the cost/requirements can be met...

Exiled Force
Paladin of White Dragon
Tribe-Infecting Virus
Magical Scientist
Cybernetic Magician
Chaos Sorcerer
Chaos Emperor Dragon - Envoy of the End
Black Luster Soldier - Envoy of the Beginning
Cannon Soldier
Catapult Turtle
Throwstone Unit
VW-Tiger Catapult
XY-Dragon Cannon
YZ-Tank Dragon
XZ-Tank Cannon
XYZ-Dragon Cannon
VWXYZ-Dragon Catapult Cannon
E. Hero Thunder Giant
etc