Can I use a GE surface burner element in a Whirlpool stove when neither the connecting ends nor the number of rounds it has match with the original?
The burner ends must match up with the design of the socket they plug into. In addition, the wattage must be approximately the same, because the heat controls (typically an "infinite switch") are designed to work with a specific power output. There may be other incompatibilities on the fancier sorts of heating elements.
If the connecting ends don't match, how are you going to use it? Cutting off the end and attaching the matching connector is a lot of work for very little benefit, as surface coil burners are not that expensive.
But in general what matters, aside from the connectors and physical size (so that it sits correctly) is the electrical specification. In a coil burner, that really is the resistance of the coil, though it may be stated in terms of Watts used or BTUs of heat generated. These burner coils are basically fancy resistors and Ohm's Law rules the day.