A - There are several ways to acheive this but all require work and commitment to duty/simming.
Consistent and quality posting always catches the eye and is the main method of climbing the ranks aboard the USS Liberator. How far you rise naturally depends on the situation - like all starships, your advancement will be restricted by the current duty staff.
If your CO or XO are removed from duty (dependant on their characters death or resignation), the vacant positions will be filled by the most capable officer available. Again, this will be determined by the previous efforts of the player in question.