Hey there, congrats! I'm glad you've seen the first results.
As far as magnesium goes, it is an essential mineral and it helps you lose weight. It's one of the supplements which Dr. Atkins suggests to aid weight loss, but as you say, some supplement sources are better than others. Dietary sources are green leafy vegetables, including spinach, broccoli, so raising your carbs a bit to increase your consumption of those will will give you magnesium and more fibre.
See here for a table with more sources of magnesium:
Dr. Atkins diet book says that you should raise your carbs in small steps after the 2-week induction period, and the reason the diet is famous is because it works.. So do what he suggests and start raising your carbs. You don't want your body adjusting to ultra-low carbs, because you'll then be stuck with a very restrictive diet in order to maintain your weight, and if you hit a plateau, there won't be much left to cut out.
There is no advantage to staying at induction levels unless your blood sugar balance is so dreadful that it goes out of kilter with the slightest carb overload. You have not had a lifetime of abusing food and you are not significantly overweight, so unless you have some sort of familial link to some health issue like diabetes, it is highly unlikely that a higher carb diet will make any difference to the diet, and it is likely to do you a lot of good.
Lower carb will not make you lose weight quicker. Your body can only burn a certain amount of fat, and better, healthier eating habits are more important than fast weight loss.
Please take the advice given by ElizEllen and me and start with the OWL stage of the diet, as in the book. Give Dr. Atkins' diet a try.