To add to what LO has said,
While I don't think you need to take the bike in to have the pedal tension adjusted if you don't know what you are doing then it is better to err on the side of caution. If you back out the tension adjustment screw too much it will bugger up the whole adjustment system. However your partner seems to have a grasp on the sport so bug his a$$ and get him to help you out!
You could upgrade but why bother. I would say use the pedals for a while right now and when the cycling bug really takes hold, then start looking at better options. You can spend any where from $50 to $300 for pedals.
The hotspots could be due to improper cleat positioning. As a starting point they should be centered somewhere near the ball of your foot. The shoes are brand new so maybe they need a little time to break in. As long as they fit properly and aren't done up too loose then they should be fine. Pay attention to where the hotspots are, it will help you identify where you may need to make your cleat adjustments. It took several rides and cleat adjustments until I finally got my speedplays set up just right for me.
Seat positioning is a matter of preference for some. LO gave you a starting point to gauge seat height. As long as when you pedal your hips are stationary and not rocking back and forth on the saddle your seat height should be just fine. Just remember pain behind the knees means its too high, pain in the front means it too low. With time your muscles and ligaments will stretch out and you can make further adjustments. Do small increments at a time to avoid injury and discomfort.
I have small hands too. So when I get in the drops my fingers don't get a great purchase on the levers. However, I spend most of my riding on top of the bars or the hoods. I'll get in the drops if I know I won't need to shift or brake for awhile. There are a number of adjustments you can make like just slightly rotating the bars up or bringing up the shifter/brake lever a about an inch (but not much more). You can even turn the hoods inward a bit to help with the comfort level. Its a matter of preference really.
And yes. Eventually anything less then 20miles will soon be a cake walk.
Good luck and keep riding.