Two fold question:

-What causes daemons to go back to the warp? Why wont they hang around and cause utter chaos when they are released from possessing a host or weapon or being summoned in a ritual?

Is there some mechanic/rule for how long they can stay?

-Is there a mechanic for heretics to prolong a summoned daemons stay? For example they know the unit of Inquisitor Storm Troopers are gonna drop in later today. Is there a way for the players to summon a daemon to face them?

1. Being in the material world is quite constricting to a daemon, consider that in the warp they can basically do what ever, in the real world they are constrained by reality and can only semi break it by using their own personal power or the power infused into them by the ritual

2. if you read the example rituals in the Core rule book they state that lesser daemons stay for 1d5+5+DOS rounds. this is extended if the daemon kills things (keep in mind its up to the GM & sacrifice is different from murder) or if the warp is thin. Additionally the Daemon may be bargained with to achieve a task, and will stay until the task is complete or they weasel their way out of it (ie. "Until the next full moon rises, slay those who seek to do me harm", a smart daemon will leave immediately as there is a full moon rising somewhere in the galaxy).

Additionally remember that the rituals in the books are only examples; modify them with the GM's permission to suit your purposes (if your character can modify them ie. Scholastic lore Occult) Ie extra difficulty for longer duration

Side question:

As we all know, Geller Fields generate a bubble of real space-time around a void ship, travelling through the warp. A Geller Field may however deactivate or even just flicker for a moment, causing a manifestation of daemonic entities on board.

What happens in case of the Geller Field activating again shortly after? Do the daemons disappear again after a brief moment, just like in the material world?

I can only assume they do, but since this is some thin-artificial layer created by the geller field, they'll still stick around for a long time, enough to cut the inhabitants of a void ship to pieces and eventually theoretically they'll disappear again.

Two fold question:

-What causes daemons to go back to the warp? Why wont they hang around and cause utter chaos when they are released from possessing a host or weapon or being summoned in a ritual?

Is there some mechanic/rule for how long they can stay?

-Is there a mechanic for heretics to prolong a summoned daemons stay? For example they know the unit of Inquisitor Storm Troopers are gonna drop in later today. Is there a way for the players to summon a daemon to face them?

Daemons usually need some sort of anchor or binding point to realspace in order to remain. Usually many will prefer to stay as part of a host albeit hating that they are confined and none like being trapped in a weapon since they can still have some manifestations of their will but they get a much lesser resistance to being forced back because they are inhabiting a body which is allowed to be here. Think of a daemon like a beach ball being held under water, the ball floats but you are forcibly holding it under and the water is pushing back against it. Eventually as your arm would start to tire holding it down your arm would slip off it and it bounces back to the surface. This is the same and eventually the daemon bounces back out into the warp.

A daemon out in the water would effectively be forced back out however if it is inside another vessel, it can stay so much longer. Many of them if free would love to cause all manner of destruction because being in a human host or any at all is often very distasteful but it's better than the alternative. The problem is though that once out in the open, the laws of reality work against them and it takes all of the daemons strength to keep itself here, which is why many have the Warp Instability trait requiring it to keep itself fed with the essence of others.

Particularly powerful daemons, ones kept topped up with essence, souls and/or blood etc or ones which are in an area of warp sensitivity can stay so much longer or in theory indefinitely until the next time they are defeated in combat which means they are banished back to the Immaterium as it is difficult to properly destroy a daemon completely. Most of them are usually banished back to return another day. If you wanted to allow the daemon to stay longer you would need to have them find ways to keep him there so there may be rituals and spells you can use to weaken the veil between reality and warp space or you may find that it needs blood and souls to stay alive longer and by it feasting on 1000 souls you might get an extra few minutes out of it etc. How you play it is up to you.

Concerning Gellar Fields, once the field is down any daemon can manifest anywhere within. Once the field is back up again, I believe they start to suffer the effects of daemonic instability as now they are effectively back within real space. It shouldn't be an immediate banishment and again the creature starts to be forced back so again its sudden submergence time. If they are quick enough and well placed, they could potentially damage the field again to maintain their presence or just simply slaughter the crew. Whichever works...

Yes, that makes sense. Even with the Gellar Fields back up, a daemon of Khorne kan keep himself in this real space by simply slaughtering crewmember after crewmember until everybody is dead, leaving the ship devoid of all life.