No, (timed)
Yes, (free)
No, (dumb)
No (first try) (it's more maths than riddle, except for figuring that the princess must be older)

Hopefully this won't spoil anything, but you will actually need to do some of the side quests in Chapter 2, in order to progress the main quest much further. If you try to push forward in the main quest, you should soon find out why. The good thing is, there are many cool and interesting side quests to choose from.

The other thing is that, if you were to go after Imoen now, you would be horribly under-leveled for those areas. Don't try to rush it :-)

You can't solve the riddle, since it has infinite solutions. You just have to check the initial conditions of each answer and select the one that satisfies the given problem. The wording is a little weird as well, which doesn't help at all :)

"A princess is as old as the prince will be when the princess is twice as old as the prince was when the princess' age was half the sum of their present age."

Let's be sexist and call the princess's current age x, the prince's current age y, the time to the future f, and the time to the past p.

"princess' age was half the sum of their present age." is the past. So
(Equation I) x-p = (x+y)/2 --> p years ago princess was "x-p" year's old.

"will be when the princess is twice as old as the prince was" is comparing the princess's future to the prince's past.
(Equation II) x + f = 2(y-p) --> f years later the princess will be x+f years old and p years ago the prince was (y-p) years old. It says twice so we multiplied by 2.

Finally "A princess is as old as the prince will be " comparing the princess's current age to the prince's future age.
(Equation III) x = y + f. Today the princess is x years old and the prince will be y+f years old in the future.

Now, we have 3 equations with 4 unknowns (variables). This automatically suggests infinite or no results. However, let's move on. We want to get rid of the time's so we can only see relation of ages

(Equation I) x-p = (x+y)/2 can be written as p = (x-y)/2 or 2p = x-y
(Equation III) x = y + f. can be written as f = x-y

now if we put this into the 2nd equation... x + f = 2(y-p)

x + x - y = 2 (y - p) --> remember 2p = x-y
2x - y = 2y - (x - y )
2x - y = 3y - x

3x = 4y

which means 3 times Princess's current age = 4 times the princess's current age. If the Princess is 40, the prince will be 30. If the Princess is 20, the prince would be 15, and so on.

I tried to make it as simple as possible. I hope I was able to achieve that to some extend :)

Edit: Fixed a small mistake.

If you don't do side quests you will miss out on some cool equipment and a lot of leveling. Your characters will be too weak to defend themselves against foes later in the story.

-edit- Also there are some places with good loot that no quest leads to. So don't be afraid to open a few extra doors and to explore all the fog.