If you look at the numbers you'll see that the ideal operating voltage and current multiplied together gives you 10 watts. 10 watts is the electrical output power you will get when the panel is pointing directly at the sun on a non cloudy day at noon on the equator. That's approximately 1000 watts per square metre landing on the panel.
Solar panels are about 15% efficient so I'd estimate that your panel is about 0.07 square metres. Given that yours appears to be about 0.1 square metres you can estimate that it's only about 10% efficient. I think typically you could expect 15% so maybe yours is a bit cheap/crappy.
So, you need to estimate how much power you might expect to receive from the sun in your location (on all days you expect it to work) and compare this with the power taken by your arduino and solenoid.
Don't get hung up on it being called "12V" - you will need to be able to regulate the voltage from a lot of panels for most applications so whether it's 12V or 20V is of no consequence. Regulation is best done by a buck converter but you might find that to get your system to work on wintery cloudy days a buck-boost regulator is needed.
The ideal operating voltage is 18 V (not 21 V) and this number gives some guidance about extracting the maximum load power from the panel but, this will change throughout the year.
My advice is buy a panel that has a decent pdf data sheet from a reputable source. The information that is provided on the ebay site would not be enough in my book.
On the question of "too much power", don't worry. As can be seen from the spec, if the panel is capable of delivering 10 watts to a load it won't deliver that power if the electrical loading is very light but, the output voltage may rise as high as 21 V. Again this tells you that a decent voltage regulation scheme is needed to both extract as much power as you can on a cloudy wintery day whilst still regulating to the required voltage when loading is light on an equatorial sunny day at noon.