Well, definitely tightly capped. You want to protect the reagent from the environment and from others stored in the desiccator. The cap isn't air tight when hand tightened, so it still very slightly exposed. You don't have to leave it loose, and hope the desiccant will dry it further.
See, desiccant simply sets up another equilibrium with the air in the vessel and the moisture its stored within itself. So old desiccant may add moisture to the local environment.
If the substance is really air sensitive, for example like butyl-lithium, then we'd handle it differently. As in we'd never remove it from the bottle, but instead transfer it with a syringe. But you don't seem to be working with that.
As for uses, it really depends on how you handle things. You have to open it so you can work with it. Otherwise, how would anyone know the reaction proceeds? How many uses you get will depend on how quickly you work. Maybe you get 3, or 5, or maybe you can finish the bottle with only minimal loss in activity. Or maybe you leave it open too long and you only get 1 or 2 uses. It really isn't easy to pin it down more than that.