Hitler could've easy won the region by sending more help to the Afrika Corp.
The main reasoning behind the Africa Korps was not to win the entire theater, but to contain the British advance. The Nazis felt, that keeping Libya was crucial for keeping Italy in the war, and they're perfectly right about this.
Owning Suez and the Levant would've meant local petroleum supplies, yes. Airlifting larger quantities of petroleum is impossible during WW2, while shutting down British naval superiority would've meant either German Panzers in London, or German Panzers in Madrid.
((Btw, Germany virtually downed it's airborne troops to concentrate enough transport planes on Sicily to be able to supply Rommel's troops there. Sending more German troops would've either meant less Italian troops, or a horrible supply situation.))
(separated from her colonial holding of India)
Nah. Most non-urgent wartime traffic UK <-> Far East went via the more secure Cape route anyways.