It is extremely difficult to apply conventional theories of time to the Chrono Universe. Its time physics follow their own laws because they were written that way. Think of every video game as being like a book from Myst: each represents a wholly independent reality which obeys the laws of physics established by its authors.
According to our physics, the Chrono Universe is either impossible or at least vastly over simplified. The details of current theory are murky, nigh impossible to verify, and still hotly debated by scientists as they comprise the core of one the most controversial issues of modern physics.
Chrono Trigger heavily involves the use of a time machine, however currently there is only one design that’s been deemed plausible. The machine design relies on a gravitational loop, which anchors the machine between two points in time (So the machine can only go as far back into the past as its creation, and only go so far into the future as the present). The loop exists for the time machine itself to exist. It cannot go further into the past than its creation because its method of transportation didn't exist thus, it cannot travel. If the Epoch was based on gravity, it could technically only move between 12,000 BC and 2300 AD (assuming that Belthazar had finished the loop at least in 12,000 BC). Odds are the Epoch does not utilize a gravity loop, but then modern physics has currently no other candidates for the job of time travel.
However, assuming that we have a vehicle capable of uninhibited time travel and using the theory of Multiverse. You could return to your time of origin with any changes you made to the past in effect. However, to change the past would be to alter your dimension. Your being is super dimensional, so you are unaffected. Killing your grandfather doesn't eliminate you; it eliminates the "you" of that dimension. In essence, by killing your grandfather, you have made a branch in time, or a slide in dimensions. Should you return to your time of origin, everything that would have resulted from actions of your grandfather has changed. You have merely traveled along the timeline of your "new" dimension. Going back to prevent yourself from killing your grandfather causes a similar dimensional shift. You can only go forward in these dimensional shifts, not back (you don't have the means). Dimensional shifts represent the "fifth" dimension of observation, or motion along and between alternate dimensions and time. (I follow with a brief outline of the dimensions)
[First dimension: a line, we observe motion along one axis; second: a single plane, we observe motion along and between two axes; third: two perpendicular planes, we observe motion along and between three axes; fourth: time, we observe the motion of motion (along and between three axes) along a single superior axis; fifth: multiverse, we observe the motion of motion (along and between three axes) along and between two superior axes; sixth: I have not capacity of explaining this, but theoretically we should observe the motion of motion (along and between three axes) along three superior axes. These are also the dimensions of physics, not of geometry. In geometry, the fourth dimension is a tesseract a.k.a., a hypercube.]
The Multiverse Theory is the application of Quantum Mechanics to macro-physics: just as a photon can occur in multiple instances, so do we occur in multiple dimensions. Just as a photon projected at a sensor is fated to land at point B, we are fated to die; however just as a photon seems to occur in multiple existences at the same time, so do we. Therefore, in one dimension the photon hits point B, and in another it hits point A (We however can still observe this and this principle lies at the heart of contemporary speculation, debate, and theory of micro-physics, and represents one of the principles that Einstein died trying to reconcile with macro-physics). So it is that our death as multiple instances to occur. We choose our course along the fourth and fifth dimensions (though we are incapable of moving backward), and Fate affects more-so the creation of alternate dimensions.
In Multiverse Theory we can reconcile Chrono Trigger. Chrono Cross, however, requires uninhibited motion between two dimensions that accounts for their respective motion along the fourth and fifth dimensional axes. For Chrono Cross to occur, sixth dimensional transportation would be required (the portal at Opassa beach which relies on the intervention of a sixth dimensional being).
For the purpose of the Chrono Universe, time gates are plausible as portals to set time periods. Their motion is linear along the time axis and thus can occur in parallel worlds. The End of Time exists in the context of Chrono Trigger, if we accept that at some point all time lines end, regardless of their dimensional situation. This endpoint exists as the End of Time and would be much like the void after a waterfall. The Bend in Time would be like an eddy, where currents from one time stream swirl, giving access to multiple time points within one dimension.
Or we could say that Chrono Universe physics are similar but different from our own because that's the way that they were written, and go along our merry way. In the end, the designers of the Chrono Universe have creative license. They can say that there exists a continent in Chrono Cross that wasn’t in Chrono Trigger. They can say that time turns lead into gold on the third Tuesday of every year in which the digits add up to 66. It’s their world. We simply chose to see it in the context of our own.