As promised, the solutions…
1. 681472 [Um, Didn’t we answer this one earlier?]
2. 3927.27272… seconds This represents the amount of time it takes the minute hand of a clock to lap the hour hand. For example, the hands coincide at midnight; they next coincide 3927.27272 seconds later, or at about 1:05:27 AM.
3. 23.14069… This is just e^π.
4. 2.1656 x 10^185 This is how many cubic planck lengths fit in the observable universe…basically, if our universe were a 3D computer, this is how many pixels you’d need.
5. 1.03 light year/year^2 This is the acceleration due to gravity g, in non-standard units. It has the following interpretation: if you ignored relativity and accelerated at a rate of 1 g (reasonable for a starship), after a year you’d have reached the speed of light.
6. 133956 This is the number of possible combinations of two birthdays, since 133956 = 366^2. If everyone on Earth had a significant other, there would be over 26,000 couples with the exact same two birthdays as you and your other.
7. About 19.5 million people The number of people on Earth who share your birthday.
8. 0.739085… This is called the “Dottie number”…an irrational number that solves the equation cos x = x.
9. 1.72048 m^2 The area of a pentagon with sides of 1 m.
10. 0.004295 % This is what percent of Earth’s history homo sapiens has been around.
Many Worlds Theory 
I shouldn’t have looked at the answers. I think it was within my ability to get #6. Number 7 is subjective, as “about 19.5 million people” is also the estimated population for Florida. OK, here was my answer to #2, which I’m sure is riddled with math errors: An arc second of latitude corresponds to approximately 101.27 feet. 3927.27272 x 101.27 = 397714.908354 feet = 397714.908354 / 5280 = 75.324.. miles. What is 75 miles away? Heaven, of course, according to the song from The Best Little Whorehouse in Texas. So that’s my answer to #2.
OK – no I know why I had no idea 🙂
For number 7, what if you were born on February 29th?
I suppose just divide my estimate by 4, so maybe 4.9 million.
But then, it’s is not every 4th year that is a leap year. The year number has to be divisible by 4, but not 100, unless it is divisible by 400.
Well, the population is just an estimate anyway, so that distinction probably falls within the margin of error.