At battalion level, yes. It might be possible for a Captain to either temporarily be bumped up to Executive Officer or else be placed in that position in anticipation of an upcoming promotion to Major.
Second Lieutenant
S1 is a staff office, not some sort of "officer class". S1 is the office at battalion and brigade level responsible for personnel management and administration.
A Staff Sergeant is a noncommissioned officer, whereas a Captain is a commissioned officer.
In most military groups a Staff Captain is an administrative officer who assists the Commander.
S2 is the code designation for the Intelligence Officer within the military. It does not directly correspond to a specific military rank, as the rank of the individual holding the S2 position can vary depending on the branch of the military and the specific unit they are assigned to. In general, an Intelligence Officer could hold a rank ranging from a junior officer, such as a Second Lieutenant or Lieutenant, to a more senior ranking officer, such as a Major or Lieutenant Colonel.
The third level of commissioned officer above the second lieutenant and the lieutenant. Mainly an administrative and strategic role of command responsible for a division of platoons reporting to the Major.
S2 is a staff office - battalion or brigade level - tasked with security and intelligence.
command sergeant major
usually assigned to a staff position. Battalion or above
S staffs are Small Unit staffs--battalion and brigade level. There is also the G staff (division and corps), the J staff (joint service--Air Force and Army officers in the same staff) and C staff (combined service--more than one nation's military).
Master Sergeants
There's a few different positions for a Sergeant Major. A Command Sergeant Major will be the senior noncommissioned officer of a Battalion or larger sized element, while a Sergeant Major will typically be in a staff position, and may serve as the senior NCO of that staff. They are primarily responsible for the noncomissioned officers under them.