In AWS, does an hour of usage get charged just for an instance being in the "running" state?
Solution 1:
Yes, your understanding is correct. There's no AWS charging based on CPU usage -- you pay the same for an instance whether its CPU usage is 0% or 100%.
Solution 2:
Yes, that's correct.
You might also look at spot instances for load sharing as they're much cheaper than on-demand instances with the drawback that they can disappear at any time. As long as you can manage that, they're a good option.