- Yes
- No
- Depends: If the summoned creature rolls a higher initiative than the one who summoned it, then it must wait till next round before it acts. If it rolls lower than the summoned then it acts as soon as it's imitative comes up even if that means going before others already in the fight.
In general, a summoned creature, and any unknown creature at the beginning of the encounter, roll normally for initiative and wait till its turn comes up for it to act. In these cases, its actually advantages to roll lower than the initiative of the person doing the summoning so that they act "faster" this round.
I'm just going to take this opportunity to tell you the current house rule that my group uses for initiatives, which has its pros and cons, but the main pro is that its easy to do and keeps the table alert, as well as makes it easy to remember who goes next.
Basically, everyone rolls initiative as normal. The person who gets the highest initiative goes first. Then we follow the order of play clockwise around the table. Any summoned monsters, or hirelings take the initiative order of the player who summoned/hired them. All monsters go during the DM's turn. There is a big drawback to this in regards to tactics, but my group has been doing it and enjoying it long enough that I had forgotten that summoned creatures don't normally attach themselves to the summoner.