Will high inrush current (30A/115V) trip a circuit breaker?
“Will it trip by circuit breaker?”

Probably not. You need to check the characteristic of your particular breaker to tell for sure, but the most commonly installed do have some time-lag for this very purpose. Since you mention 115 V, I assume you are in North America. I don’t know how they are marked there but on this side of the pond they come in “speeds” A-D, with C being the most common.
 

“How long does the inrush current last?”

It should last some tens of ms or a few cycles. 


“What does cold start mean in a power supply?”

Cold start means your power supply is completely deenergized, say 30 seconds after you have turned it off. A hot start on the other hand would be flicking it off and then on in rapid succession.