Does the value of my Bitcoin fluctuate automatically? If you own a small amount of Bitcoin (say,$10) does one have to "invest" it somewhere for it's value to change or will the $10 fluctuate by just sitting in one's wallet and one can see the value fluctuate by checking the wallet from time to time?
Whether it fluctuates or not depends on how you express value. If you happen to be one of them American folks, who use dollars to express value, then a fixed amount of money in other currencies (such as euros or bitcoins) will fluctuate.

But similarly, a $10 dollar bill will fluctuate in value, if you express value in euros or bitcoins (basically, that is if you live anywhere on the planet except the US).

It's all a matter of perspective.