Consultas básicas de MySQL

Puede probar las consultas en http://sqlfiddle.com/#!9/839d2/1

Consulta 1

Lista de todos los planetas que tienen capitanes. Muestra id_planet, planet_name, capitanes totales en cada uno de esos planetas, así como la cantidad de batallas (si las hubo) que tuvieron lugar allí.

SELECT DISTINCT aa.id_planet, aa.planet_name, _aa.captains_count, _bb.battles_count
FROM planet AS aa
INNER JOIN soldier AS bb
ON aa.id_planet = bb.planet_id
INNER JOIN (
    SELECT planet_id, COUNT(*) AS captains_count
    FROM soldier
    WHERE rank = 'captain'
    GROUP BY planet_id
) AS _aa
ON aa.id_planet = _aa.planet_id
LEFT JOIN (
    SELECT id_planet_battle, COUNT(*) AS battles_count
    FROM battle
    GROUP BY id_planet_battle
) AS _bb
ON aa.id_planet = _bb.id_planet_battle
WHERE bb.rank = 'captain';

Puedes tener los mismos resultados usando esto:

SELECT DISTINCT aa.id_planet, aa.planet_name,
(
    SELECT COUNT(*)
    FROM soldier AS _aa
    WHERE _aa.rank = 'captain' AND aa.id_planet = _aa.planet_id
    GROUP BY _aa.planet_id
) AS captains_count,
(
    SELECT COUNT(*)
    FROM battle AS _bb
    WHERE aa.id_planet = _bb.id_planet_battle
    GROUP BY _bb.id_planet_battle 
) AS battles_count
FROM planet AS aa
INNER JOIN soldier AS bb
ON aa.id_planet = bb.planet_id
WHERE bb.rank = 'captain';

Consulta 3

SELECT aa.name, aa.rank, bb.planet_name AS planet_from, (
    SELECT COUNT(*) 
    FROM soldier AS _aa 
    WHERE _aa.planet_id = aa.planet_id
) AS number_of_soldiers, 
(
    SELECT COUNT(*)
    FROM battle AS _bb
    WHERE _bb.id_planet_battle = aa.planet_id
) AS number_of_battles
FROM soldier AS aa
INNER JOIN planet AS bb
ON aa.planet_id = bb.id_planet;

Aquí, no utilicé Joins para calcular number_of_oldiers y number_of_battles como lo hice en la Consulta 1.1 porque sería una subconsulta correlacionada y, como tal, no podría tener acceso a las consultas externas (https://dev.mysql.com/doc/refman/5.5/en/from-clause -subconsultas.html ).

Consulta incorrecta:

SELECT DISTINCT aa.id_planet, aa.planet_name, _aa.captains_count, _bb.battles_count
FROM planet AS aa
INNER JOIN soldier AS bb
ON aa.id_planet = bb.planet_id
INNER JOIN (
    SELECT COUNT(*) AS captains_count
    FROM soldier AS _aa
    WHERE _aa.rank = 'captain' AND aa.id_planet = _aa.planet_id
    GROUP BY _aa.planet_id
) AS _aa
ON aa.id_planet = _aa.planet_id
LEFT JOIN (
    SELECT COUNT(*) AS battles_count
    FROM battle AS _bb
    WHERE aa.id_planet = _bb.id_planet_battle
    GROUP BY _bb.id_planet_battle 
) AS _bb
ON aa.id_planet = _bb.id_planet_battle
WHERE bb.rank = 'captain';

Entonces, la consulta anterior es incorrecta y produce el error:Columna desconocida 'aa.id_planet' en 'cláusula where'.

En cuanto a la segunda consulta que solicitó, espero que alguien más pueda intentarlo.