How do I calculate current usage from two sets of 5050 LED lights of varying lengths?
You're right to be confused because the figures given don't tie up. 10.8W per metre at 12V does indeed give you 4.5A for the 5 metre length and 9A for the 10 metre length. So which figure should you take? It's not uncommon for listings on eBay to be wildly inaccurate, possibly just cut and pasted from another listing or badly translated so the answer is... neither.

Measure the current consumption and rate your supply accordingly. If you don't have a basic multimeter, and you're planning to play around with things like this, get one - they're widely available at budget prices. The alternative is that you end up overloading your supply; if it's a cheap one with no overload protection and you're lucky it will just quietly fail, if you're not it could overheat and start a fire.

As both sizes are designed to run from 12V you simply connect them in parallel to a 12V supply and add the currents together, then pick a supply that can comfortably deliver that load; I'd suggest allowing at least 25% overhead for safe and reliable operation.

Provided the different sizes are designed to be the same brightness when powered at the same voltage, then yes they will be the same brightness when you put them in parallel.

Incidentally, LEDs are not linear devices so the concept of resistance doesn't apply to them. Some even have regulators built in and won't behave like resistors at all.