1. Yes - enlisted persons can compete for Appointments to USNA. If you graduate from USNA, you will be appointed as an officer in the US Military - you would not then attend OCS (though I am pretty sure there is a process even USNA graduates that accept a commission in the USMC must complete)
2. I think the age limit of 23 that you reference is the maximum age you can be upon entry to USNA.
3. You will be hard-pressed to find an enlistment option for a single year. Whatever contract you would sign to enter the USMC would be waived if you were to receive an appointment to USNA. However, if you were not able to earn an appointment you would be obligated to complete your enlistment contract, so be prepared to serve your entire enlisted contract.
4. Beware of any USMC recruiter that paints the enlisted to USNA route as an easy one - there is no easy route. There are few spots available relative to the number of people pursuing them at USNA.
5. There are other paths to commissioning especially from the enlisted ranks. Pretty sure all require a 4 year college degree and all do require US citizenship.