1 week of cycling is insufficient.. Min, 1 month and u need to check the parameters although u are using NSW.
1) For a 10Gallon tank, its ok to use a skimmer, but i dont find it usefull coz regular water change will do the work.
2) what kind of LED are u using? watts per LED? Cree Led? Diffrent LED have diffrent Par Value.
3) No.. 24/7 will cause tank problems such as Algae problems. Run 9 - 11 hours depending on ur LED