H, I'm not sure about the medication but I'm glad it's workin' for you. The normal amount of times to urinate on average is about 6 but it depends on a lot of things such as how much water they drink and the size of their bladder. Don't feel afraid if you urinate a few more times than that, anxiety can make you go to pee more often. It's only when you're going to the bathroom every 30 minutes that you should be worried, bring it up with your GP to calm your mind though.
The first time you urinate for the day is often a darker yellow, the darker your pee is the less hydrated you are, basically. Because you've been sleeping and haven't drank water for a while it's pretty concentrated, don't worry about it and just drink some water. As long as your urine isn't red or something I don't think you have too much to worry about, a clear and slightly yellow urine is absolutely fine.
If your lips are dry do you often lick or bite them? If you do, leave them alone and drink plenty of water and they'll start going back to normal after a while. What do you mean by your pinch your skin back and it goes back to place? Do you mean you just pull the skin back on your hand and once you let it go and returns? If so that's fine, I'd be more worried if it didn't.