It just has to burn more fuel for each combustion cycle to keep the engine spinning at the same speed. It's like how it's easier to pedal a bike down an incline versus up the same incline, but your legs will still pedal at the same rate for the same speed (assuming you don't change gears).

No, because an engine can use different amounts of fuel even at the same RPM. At the most extreme, a car can go downhill at high RPM with no fuel injection at all, only driven by gravity.

During normal driving, the engine's crankshaft has a hard link to the wheels. It's going through a couple of gears etc. inside the transmission etc., but the speed conversion from that is fixed within a single gear. This means that the speed the vehicle is going is directly tied to the RPM the engine is turning at. For every gear, every possible vehicle speed correlates directly to a single specific RPM of the engine. Fuel use at that RPM can vary a lot though, entirely depending on the amount of energy needed to keep the engine at that speed with air resistance and other factors trying to slow the car down through the drivetrain.