When do summoned monsters act (disregarding the first round), and can a Pathfinder Summoner, using their Summon Monster spell-like ability, choose to delay until after this in order to summon a second monster using their spell-like ability and have it act also in the same round? For example, I have a summoned monster out from a previous round, and on my turn I delay until after it attacks and then summon a second monster which then replaces the first monster and attacks. So effectively I get two lots of monster attacks in one round.
Probably so by RAW and yes in practice.
The reason a summoned creature takes until the beginning of your next turn to act is because that's when a one-round spell comes into effect: the creature is not present before then.
A spell that takes 1 round to cast is a full-round action. It comes into effect just before the beginning of your turn in the round after you began casting the spell. You then act normally after the spell is completed.
Therefore, using the Sp as a standard action allows the usual rules of spell effect timing to control: the creature arrives as you finish casting, on your turn, and acts immediately, potentially before the remainder of your actions on that turn.
It's less clear whether the summoned creature acts on a potentially independent initiative count in later rounds (since it says that it "acts on your turn", but not that it always does), but one could argue that the ability to instruct the summon to take various actions, including delaying or readying, would imply that.
In any case, though, even if the creature acts on your turn, simply readying an action to summon a new one once it has finished its next attack sequence will do the job in essentially all cases. A readied action takes place outside your regular turn, so there is no problem there.
Summoning a creature as a spell takes a full round (barring some other ability that lets you summon more quickly). That means that you start summoning on your turn in round 1, the monster appears on your turn in round 2 and may act, and the summoner may then do something else in round 2 as well. Summoning as a Summoner ability takes a standard action, but dismisses any existing summons. You are probably talking more about the latter ability, but be advised that you can mix and match - so if you do a Summon SLA and then a Summon spell you can also do "summon stacking" without delaying (though it takes till round 3 to get going).
After the round a summon appears, you're all just creatures, treated individually and equally like anyone else in the initiative order and game rules. You can delay till past your summoned monster's turn and when your turn comes around perform another summoning (dismissing the creature that just acted) to get two summoned attack routines in that round, at the cost of quickly novaing through your summons for the day.
Do keep in mind that if you delay and you need to order your monster to do something else, you may have jacked yourself - only being able to give it new orders after its action has gone by.