Even though it isn't really milk (in the dairy sense), coconut milk still naturally separates into a thick cream and thinner liquid like regular milk. As such, when working with coconut milk you should still follow the same procedures you would to make a milk-based cream sauce.
The number one rule when making any creamy sauce is: DON'T LET IT BOIL! Boiling will guarantee that your creamy sauce (including sauces made with coconut milk) will break in some form or fashion. At most, you should cook these at a bare simmer.
Other than that, there are some techniques you can use to keep your curry smooth.
You could use an emulsifier like honey (common in vinaigrettes, where it is used to make sure the oil and vinegar don't separate), added toward the end of cooking.
You could also use a thickening agent, like a cornstarch slurry or a quick roux. Curry paste is also a thickening agent. As a general rule of thumb, when making Thai-style curry I usually cook my vegetables in a little more oil than I think they need, then add the curry paste and sauté that until it has absorbed the oil (along with any dry spices). It will act as a roux for the coconut milk and make sure there are no lumps in the final curry.
Lastly, cooking the curry uncovered at a simmer, stirring occasionally, will thicken it up nicely and help all the ingredients stay together.
Indian curry traditionally has - in addition to the ginger, turmeric, cumin and chili (I assume you mean chili powder) that you used - a generous amount of garam masala, coriander powder, and garlic.
Sometimes you'll see "curry powder" used in recipes instead of garam masala; they are similar but not exactly the same.
Either one of these would be fine, and arguably the most important missing ingredient here. I'm not even sure you could legitimately call it a curry without one of the above.
Depending on your spice tolerance, you might need to add more chili powder as well.
Note that most spices in a curry will need to be heated before they'll really release their aromas (and therefore flavour), so you can't just add them cold, and I definitely don't think you'd want the taste of raw garlic/ginger in your curry, even if it is presently tasteless. Give it a good simmer after adding some garlic (powder is fine) and garam masala or curry powder and you might be able to salvage it.
Or you could try heating the new spices dry, for a very short time, to give them a bit of a head start aroma-wise; just be very careful not to burn them.
Best Answer
There is nothing inauthentic about using sugar in an Indian dish, even a savory one. For example, Gujarati cooks often add raw sugar (jaggery) to daal and curries. Quoth Wikipedia:
"It is common to add a little sugar or jaggery to some of the sabzi/shaak and daal. The sweet flavour of these dishes is believed to neutralize the slightly salty taste of the water."
And here's an example Gujarati potato curry recipe, which includes a tablespoon of sugar.
As for how much to add, that's a matter of your taste and the level of acidity and/or saltiness in the dish. My Gujarati friends in Boston like stuff rather sweeter than I would personally prefer, so be cautious.