Welcome to vaping. I will try to answer some of your ?'s
Yes, this dizzyness will go away. Or if it doesn't then try to lower the nicotine dose.
Your kit came with a bottle. Im assuming that is your juice. Usually you will add more liquid when you start to lose the vapor/taste, and sometimes will get a burnt taste. That simply means your out of juice, and will need to add more. I would recommend dripping 3 drops directly on the atty. Drip, Vape, repeat!
I think the battery will last roughly 2 hours on your kit.
I would charge the batteries as soon as they go dead, just so you will have a fresh one when the other dies.
Hope this helps.