Does the following diet pose any health risks?
1) Eat very low carbs (less than 30 grams per day) for 6 days a week.
2) Load up on carbs on the 7th day of the week, to keep metabolic rate high
3) Ignore calories or fat content, and expect higher than average sodium intake.
Well...the whole point of eating low-carb is to get your body to switch over to using stored fat for energy instead of glucose. Loading up on carbs isn't really going to help that, and it's not going to "speed up your metabolism," either. Carb-loading is generally used to maximize the amount of stored glycogen in your body prior to some athletic event. That being said, if you use the high-carb meal as a sort of "cheat meal" to satisfy a craving for carbs...I doubt a single day or meal is going to derail the low-carb train, but I'd question the psychological aspects of holding back something you're trying to avoid as a reward. It seems like that might be counter-productive over the long term.
As far as calories are concerned, obviously there's a point at which excess calories will be harmful, regardless of where they're coming from. If you're trying to lose weight (I'm assuming you're male), 1500 kcal/day is probably a good target, paired with the low-carb strategy over the medium term (6 weeks).
Over the long term, the only thing that's going to work as a weight-loss strategy is a complete and lasting change in your diet and exercise habits, unfortunately. I believe just about every intervention ever proposed fails without that. Even people with gastric banding, sleeve gastrectomies, and gastric bypass eventually start gaining weight again, because over time they develop new ways to eat the same amount of the same bullshit they were eating before. I say unfortunately because, well...it just doesn't happen that often. Maybe something like 5-10% of people who go through prescribed weight-loss regimens actually manage to keep the weight off.
Now, if you're not trying to lose weight or anything, I don't think there's much of a point in going low-carb. You definitely want to go with starch (glucose polymer) over sucrose (glucose-fructose disaccharide) carbs, though. I'm pretty firmly convinced that our ability to metabolize fructose is limited, and has some pretty catastrophic effects with respect to metabolic syndrome, atherosclerosis, etc.