Wolverine clearly neither knows nor cares about temporal mechanics. Presuming that these are indeed the young X-men of Earth 616 and not an alternate timeline, then it is vital to the time stream and the history of the entire X-men concept past, present and future that:
1. Wolverine does NOT kill the young Cyclops.
2. IF any of the young/original X-men die here in the present, then the past is forfeit and the time-stream will reform itself accordingly. How many super-villains/threats would have succeeded had the original 5 X-men not been there to stop them?
3. Regarding Beast opening his memories to Jean for her to learn everything, that is indeed a calculated risk. He is counting on the fact that when the originals return to the past that Xavier of the past will memory wipe them. Unfortunately, given all that they will see and learn such a memory wipe will be tricky and likely not 100% thorough or permanent. Also Beast is forgetting that the Xavier of that era cannot mindwipe himself, therefore as Xavier is scanning for the memories of the future to erase from the original 5 minds, Xavier himself will learn of the future INCLUDING the fact that he will be killed by Cyclops. How would such knowledge affect Xavier and how he trains them and teaches them as well as the new X-men he recruits? Xavier will have to face a choice: change things and hope the outcome is better or sit back and let things ride even though he knows he will be killed by his prodigal son....unless Xavier uses this foreknowledge to avert his death in that final fight.
Remember Beast Wars? Once they found out they were on ancient Earth and that the Autobots and Decepticons had already crashed and were dormant for the next 4 million years it became a fight for temporal survival. When Predacon Megatron absorbed the spark of the original Megatron, Primal had to ensure that Pred Megatron survived in order to be captured and return the original Megatron's spark otherwise the timestream would wipe out and change the Cybertron that they came from.
Remember Babylon 5? Commander Sinclair becomes Entilzah/Ranger 1 and rebuilds the Rangers on Mimbar then learns of his true destiny and has to go back in time and steal Babylon 4 and take it 1000 years back in time to fight in the previous Shadow War. Sinclair tells them all that he will take the station back because he already has and always will, his life was literally a temporal circle that could not be broken. Once in the past and assuming the form and name of Valen he then helped defeat the Shadows but also had to deal with the fact that if he changed anything, such as leaving a message to Delenn to warn her to avoid the Earth-Mimbari War, that there would be no Babylon stations as their construction was a result of that war hence no Babylon 4 and no Valen and thus the Shadows win. Now imagine if Sinclair was killed somehow BEFORE he went back in time with Babylon 4 to become Valen? Shadows win.
Theoretically, the original 5 can stay here in the present as long as they want but:
1. They must NOT die
2. They must have their memories wiped prior to returning to avoid Xavier learning of the future
3. OR: they must return at the exact second that they left thus they technically never left and thus their memories of the future should be gone.
Reed's proven theory where you can't really change the past, but create another timeline that co-exists which was proven by the Thing when he went back in time to give his younger and dino-hided self the cure which changed nothing for the present him.