If you have met the conditions of your LOA, including having a nomination, you will receive an offer of appointment. If your plan B is in place, then there may be no need to continue working on additional applications. Bear in mind, every year, there are candidates with offers of appointment who later become disqualified, medically or otherwise.
The answer is almost certainly yes. However, you will know you are in when your portal shows your offer of admission. You are not "in" until that change is reflected. As mentioned above, continue to work on your plan B. Unusual circumstances do occasionally occur (like someone getting seriously injured) before R-Day that costs them their appointment. So always have an alternative right up until you are ready to report.
I am VERY certain that you will receive an appointment, but I would not stop completing applications to other schools regardless. It is very, very rare that an LOA recipient will not receive an appointment, but it has happened. I personally know a USNA applicant who received an LOA, however, due to an injury after he was fully qualified unfortunately did not end up receiving the promised appointment. As the others have said, always have a back up!