I caught a swarm, how long till I inspect.

[Antipodes]

pollen comes into a hive regardless of whether they are queenless or not
Bees are opportunists if there is pollen available they will bring it in and store it for later

Yes, as I said above...
"If you haven't seen pollen coming in regularly and then you do, I've found that that signifies the commencement of egg laying. You can also get pollen coming in with brood with laying workers and sometimes I've seen the odd bit of pollen coming in with neither queen brood or laying worker brood."