As I have said before, Daddy was the welder. Not me!
But, having watched and "assisted" for the first 25 years of my life; I feel confident enough to answer this.
You are right about the heat settings and material thickness, more for more and less for less.
For the questions about flux core vs solid wire, they make and sell both types. Most that do solid core also can weld with flux core. The inverse is not always true. It is cheaper and easier for the manufacturers to make a dedicated flux core welder, no regulator or gas solenoid involved.
Duty cycle: this is vitally important when choosing a welder for purchase. If you only have a minimal budget, and limited electrical capacity, don't get in too big of a hurry welding. The 120V welder a will get the job done, but not nearly as efficient as a Lincoln SA200. You don't see too many pipeline welders with a Blue machine in the back of their truck. Duty Cycle is how long you can weld at a given setting for a given period of time. More is better. An understanding of the duty cycle will keep an owner from cursing and kicking their machine. It's not its fault, it's the fault of the internal capacitors contained where you can't look at them.
Not trying to fault machines that can run on a 30amp circuit at 120V, they have a place and will suffice for most tasks. That being said, read the fine print and buyer beware!