You should be just fine. The yeast nutrient is a plus, but not a necessity. Add when you pitch to your wort. Your stir plate is mixing in enough oxygen. Again, if you have the capability of adding oxygen, do so when you pitch the yeast to the wort. Covering the starter isn't really necessary. Most brewers decant their starters before pitching so that you're adding just the yeast with as little of the starter 'beer' as possible. You're making yeast, not beer, with the starter and can get off flavors that are best not added to your wort. If you can keep the stir plate with starter away from light that would be good, but not critical.