Ok, I read all that so let's cut to the chase... Is the Sun going to burn out soon and should we all buy gold?
There is a school of thought which asserts that the Sun cycles between two states -- fusion, and non-fusion -- and that it is currently in the non-fusing state.
According to this theory, the Sun, while it is in its fusing state, heats up, and expands, until it reaches the point at which it is no longer producing enough pressure (due to gravity) to sustain the fusion reaction. It then stops fusing, begins cooling off, and thus contracts. When it contracts to a certain point, fusion begins again, and the cycle repeats.
The evidence generally given in support of this theory consists of the cyclical ice ages, and, the "Missing Neutrinos". (The Sun, if it was fusing, would be producing more neutrinos than are currently being detected. That's right -- according to this theory, the Sun is not in its fusion mode, and we are headed toward an ice age -- one which, according to various "bits of history" we are somewhat overdue for.)
The question of "What about the missing neutrinos?" is one that we are told is answered -- by stuff that to an ignoramus like me :) sounds a wee bit too esoteric, a bit too hopeful, a bit too... unconvincing.
My guess is that the jury is still out on the theory. But to answer your question, if the Sun is in a non-fusing condition, it's only temporary. Stick around a few thousand years and everything'll be fine again (but stock up on SPF-off-the-charts for when that happens!)