Maybe. Who told Parson he could speak again?
Are you sure? It could be implicit, it could have been mentioned in between panels or it could have been the first question ("What would you do if you had to defend a fortified city against...")Again, he wasn't actually given any such order.
Any time from summoning to Tools departure seems legit to me, as long as no one has given an order to countermand it. At least Tool didn't give one.
It could be a dozen of other reasons also, one being Parsons competitive nature. Who knows?