Should Germany take Egypt first turn?
Yes, of course!
Without an attack of the german africa-korps, the italians will never be able to take Cairo - at least not in Round 1.
Additionaly, you place your transport in a good spot for further attacks in russia or africa should it survive. There is a good chance of destroying all british forces in Egypt and even the possibility of conquering it. Furthermore it opens up opportunities for Italy in africa - even though italian assistance may be better applied in russia.
Should germany commit planes in Egypt?
No! germanys 1st turn is the most important turn of the whole game. Commiting the german bomber just to destroy one plane is a misplacement of forces. The german airforce should IMHO be commited to destroy the royal navy.
1. Send 1 submarine, 1 fighter, one bomber to seazone 2 to sink the Hood and its transport
2. Send 1 submarine, 2 fighters to seazone 12 to sink 1 cruiser, 1 destroyer
3. Send 1 submarine, 1 fighter to seazone 6 to sink 1 destroyer
The germans should build an aircraft carrier. With these attacks, the british player has to rebuild the navy from space one without the royal air force being able to sink the german fleet.
(Side note - building a destroyer and subs might also repel the royal air force bringing losses to the RAF and the subs diving after losing the surface ships. Building a battleship and a submarine is extremely expensive. I still propose building the carrier as it will allow the transport to survive.)
British 3 bomber built. (and sinking the italian navy in B2)
Sinking the italian navy does not threaten the german. If the german built one additional transport in his second turn the second british built will have to fortify the United Kingdom. The italian will start putting out infantry and relieve the german forces from defending France further increasing the pressure for russia. Nothing has been done to stop japan from taking africa. His majestys navy will never
Pros - Italy will stop threatening africa and never get major IPC.
Cons - GB will not have a navy and Germany can withdraw its forces from the western theatre.