they cannot use drive charge to power anything, its static
electricity, it would blow out the ship systems if they did that, if not
torch the people in it. It would be like unleashing lightning into the
ship systems just to clearify the point.
Yes, but lightning can be harnessed, if you have a key and some string.

Seriously, wiht all the tech they have, I can't imagine they couldn't figure out some way to safely draw off a static charge, at the very least discarding it, but ideally storing and/or burning it as fuel.
also, the fuel mechanic in the game is not represenative of what the
codex says is going on in relation to how travel actually works, Fusion
reactors only need to be refueled every coupld of years, and running of
ion engines, anti-proton drive, etc, doesn't use fuel per se.
The way it's depicted in gameplay doesn't relate to what the Codex says, but that could just be a display issue. I mean, to accurately reflect the codex entries, you'd need to chart a course from one system to another, similar to relay hopping, and then it would just show the ormandy accelerating to the midpoint and then decelerating to the destination in a smooth motion. In practice you just "putter around," but for the point of argument this might just be a simulation for the player's benefit that does not accurately reflect what's happening. In either case, the fuel use would be the same either way, if we assume that they are trying to maintain maximum speed and not conserve fuel by coasting.
they already DO coast, the 12LY/day limit, is because they
accelerate to 12 LY and stop accelerating because any faster and it
would saturate the core faster. THERE IS NO SPEED LIMIT IN SPACE, its
about acceleration not speed.
An interesting point, but perhaps the "12 ly/d" thing is meant in the sense that since they DO need to stop for discharging every few days, if you take the maximum distance they could achieve in that time, and then average it out, it would be 12yr/s. Presumably they could reach a higher top speed along the way. Perhaps if discharge limitations could be removed then they could accelerate well beyond that listed speed.
FTL drive cores can only operate for 50 hours, and then must be
discharged, which can take several hours to days depending on the
discharge site.
This also wouldn't make sense. If it's an electrical charge then moving it from place to place should be fairly instantaneous.
while they may have an understanding of the physics involved,
scaling it up as you say, well that's the billion credit question..
But not impossible. My point is not that it would be super easy, or they would have done it already, it was just that they aren't complete black box technology, they grasp the fundamentals. Also, since the destroyed relays were still relatively intact, and they've never had the opportunity to study even broken relay bits before, they can get a real head start on making new ones.
yeah, i saw that he was talking about the control ending. And yeah they do explode the same EXACT way.
Mass Effect 3 Ending Comparison.
it's the Citadel that doesnt get torched.
Perhaps he just mis-spoke then, I wouldn't take that comment as confirmation that they're actually ret-conning the relay's destruction just yet.
I never thought of it this way. It is important to remember the
relays were not made for the Reaper's travel convenience, they were made
for the Reaper's reaping convenience. As is, the relays are convenient
enough for organics so that they don't bother developing alternatives,
and it has the added benefits of dictating where organics colonize and
being easy to control via the citadel, aka ground zero in every reaper
cycle.
If a better way exists, I can see the reapers not bothering with it if it would make the reaping cycle harder.
And if the Reapers had better tech, they wouldn't let the organics
know about it, because the entire point of the relays is that the Reapers can shut them down at will, bottling in a previously galactic society and making them easy for the picking. For all we know, some prior civilizations did develop better FTL, but if so the Reapers would have done their best to erradicate that knowledge.
The solution then, is to have electrostatic ion thrusters
supplementing whatever other propulsion system the ship uses; and make
sure that the paths from the element zero core to the ion beams are more
conductive than the paths from the core to the hull. The negative
charge in the core will naturally discharge continuously into the
positive ions emerging from the thrusters; both enabling the thrusters
to function, and preventing static build up within the ship. 
Definitely an interesting idea. I remember watchng a show about the ion drive on the Hayabusa probe, so that's something we actually have already.