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When a star has finished fusing all its hydrogen into helium, it will then start fusing helium into beryllium and so on and so forth up until iron.
When the star is fusing to beryllium, will the star still be in the main sequence phase and will it at that point start to grow into the red giant phase, or is there no given rule for when it will start growing?
Does a star fuse helium to beryllium on the main sequence?
Stars don't fuse helium to beryllium except as a very, very short intermediate step toward carbon. Helium-helium fusion to form beryllium is endothermic: It consumes energy. To make matters worse, the beryllium-8 that results has an extremely short half-life, less than $10^{-16}$ seconds. Helium would be the end of fusion in stars (and there would be no us) if not for a fluke: The beryllium-8 formed by helium-helium fusion has almost exactly the same energy as does an excited state of carbon-12.
This greatly increases the probability of a third helium-4 nucleus combining with a short-lived beryllium-8 nucleus to form carbon-12. This is stable. The next stage after hydrogen burning is thus triple helium burning (the triple alpha process), essentially bypassing beryllium except as an intermediary.
When the star is fusing to beryllium, will the star still be in the main sequence phase and will it at that point start to grow into the red giant phase, or is there no given rule for when it will start growing?
A star leaves the main sequence well before it starts fusing helium. It leaves the main sequence when the star can no longer sustain hydrogen fusion in the core. This happens when the core becomes void of hydrogen. At this point, the helium left behind by hydrogen fusion is essentially ash. Hydrogen fusion proceeds on the edge of the core (shell burning), but the hydrogen-depleted core at this point is far too cold to fuse helium to carbon (not beryllium). So it collapses, and gradually becomes hotter.
The star starts fusing helium to carbon (and also oxygen) if the post main sequence star's mass is large enough. At this point, the red giant collapses and behaves almost like a main sequence star with a second life. That second life doesn't last very long, however.
Main sequence stars are characterized by hydrogen fusion in their cores, either through the proton-proton chain (for lower-mass stars) or the CNO cycle (for stars more than about 1.5 times the Sun's mass). Outside the core, no significant fusion takes place; the outer layers are involved in radiative or convective energy transport, but not energy generation. In general, if hydrogen fusion is occurring in the core, we say that a star is still on the main sequence.
This changes in stars that evolve off the main sequence. Some low-mass red giants may fuse hydrogen to helium via the CNO cycle in a layer outside a largely non-reactive helium core; this is referred to as shell burning. In more massive stars, heavier elements (e.g. helium, carbon, etc.) are fused inside the core, and shell burning continues in the outer layers. For instance, in a fairly high-mass star that is far into the post-main sequence phase of its life, you might see oxygen, neon, carbon, helium and hydrogen being fused in successive layers farther and farther from the core.
A common misconception is that a star uses up all its hydrogen before leaving the main sequence; this is not true. It merely uses up the majority of the hydrogen in its core; there is still plenty in the outer layers, which is what makes shell fusion possible.
Let's consider stars of around one solar mass. As hydrogen fusion stops in the (now degenerate) core, the source of pressure keeping the star in hydrostatic equilibrium vanishes. Hydrogen burning starts in a shell around the core. After some time, the core begins to contract, the outer envelope expands, and the star is said to be on the red giant branch. Eventually, temperatures rise to the point where the triple-alpha process can occur, and a helium flash occurs, marking the beginning of the horizontal branch and helium fusion via the triple-alpha process. Hydrogen shell burning continues.
As you'll notice - and as others have said - stars don't fuse helium to beryllium to any significant degree during any part of this process, or post-main sequence evolution in general. It's endothermic; the triple-alpha process is exothermic.
