Hi Acron
Everyone's different so we can't tell you how many units you need, but I wouldn't expect 4 units of Levemir to last 24 hours. With Levemir, smaller doses don't last as long as bigger ones, so you may need a second dose, maybe at breakfast. Low carbing shouldn't affect your Levemir dose much because your mealtime bolus should be dealing with the carbs. The Levemir should be holding your bs stable day and night assuming you didn't eat.
A ratio of 1u for 10 carbs is a starting point from which to adjust. You're right that you need to get your basal sorted first, otherwise you could end up constantly compensating for insufficient Levemir with artificially big bolus doses.
Correcting means knowing how far 1 unit of bolus will reduce your bs and thereby how much extra you need to reduce your bs to the desired level without going hypo. (The correction dose is on top of anything you're injecting to cover food.) Generally corrections are done with meals and at bedtime, although once you know your own ratios inside out you may be able to correct sooner. If you jump in and correct too soon after a meal, the doses can overlap too much and cause hypos. You could start by assuming 1u reduces by 3mmol and see if that works, though you may need more units for the same reduction if bs is very high (about 14 or more) to start with. The beauty of this is that you can correct an unexpected high bs and still know what your bs would have been if you hadn't corrected it. Therefore you can see trends without tolerating high bs for days before making a change.
Similarly if you know 10 carbs raises you by 3mmol, then you know how many extra carbs to eat to adjust a low bs up to where you want it.
Can you adjust your doses by half-units? If not, ask your nurse about half-unit pens. At low doses, these make a fantastic difference, especially with the Levemir. The usual increase/decrease step is about 10% of the dose - whereas to adjust your Levemir from 4 units without a half-unit pen you'd have to increase or decrease by 25%. Things tend to be more stable overall if the basal is just right and a half-unit pen gives you more scope to tweak it.
Sorry there's no quick answer, it really is a case of trial and error.