Better query
Fix the syntax, simplify and clarify:
SELECT *
FROM  (
   SELECT p.person_id, p.name, p.team, sum(s.score)::int AS score
        , rank() OVER (PARTITION BY p.team ORDER BY sum(s.score) DESC)::int AS rnk
    FROM  person p
    JOIN  score  s USING (person_id)
    GROUP BY 1
   ) sub
WHERE  rnk < 3;
Building on my updated table layout. See fiddle below.
You do not need the additional subquery. Window functions are executed after aggregate functions, so you can nest it like demonstrated.
While talking about "rank", you probably want to use rank(), not row_number().
Assuming people.people_id is the PK, you can simplify the GROUP BY clause.
Be sure to table-qualify all column names that might be ambiguous.
PL/pgSQL function
I would write a PL/pgSQL function that takes parameters for your variable parts. Implementing a - c of your points. d is unclear, leaving that for you to add.
CREATE TABLE person (
  person_id serial PRIMARY KEY
, name text NOT NULL
, team text
);
CREATE TABLE score (
  score_id serial PRIMARY KEY
, person_id int NOT NULL REFERENCES person
, score int NOT NULL
);
-- dummy values
WITH ins AS (
   INSERT INTO person(name, team)
   SELECT 'Jon Doe ' || p, t
   FROM   generate_series(1,20) p                   -- 20 guys x
        , unnest ('{team1,team2,team3}'::text[]) t  -- 3 teams
   RETURNING person_id
   )
INSERT INTO score(person_id, score)
SELECT i.person_id, (random() * 100)::int
FROM   ins i, generate_series(1,5) g;               -- 5 scores each
Function:
CREATE OR REPLACE FUNCTION f_demo(_agg        text DEFAULT 'sum'
                                , _left_join  bool DEFAULT false
                                , _where_name text DEFAULT null)
  RETURNS TABLE(person_id int, name text, team text, score numeric, rnk bigint)
  LANGUAGE plpgsql AS
$func$
DECLARE
   _agg_op  CONSTANT text[] := '{count, sum, avg}';  -- allowed agg functions
   _sql     text;
BEGIN
   -- assert --
   IF _agg ILIKE ANY (_agg_op) THEN
      -- all good
   ELSE
      RAISE EXCEPTION '_agg must be one of %', _agg_op;
   END IF;
   -- query --
   _sql := format('
   SELECT *
   FROM  (
      SELECT p.person_id, p.name, p.team, %1$s(s.score)::numeric AS score
           , rank() OVER (PARTITION BY p.team ORDER BY %1$s(s.score) DESC) AS rnk
       FROM  person p
       %2$s  score  s USING (person_id)
       %3$s
       GROUP BY 1
      ) sub
   WHERE  rnk < 3
   ORDER  BY team, rnk'
    , _agg                                                                 -- %1$s
    , CASE WHEN _left_join THEN 'LEFT JOIN' ELSE 'JOIN' END                -- %2$s
    , CASE WHEN _where_name <> '' THEN 'WHERE p.name LIKE $1' ELSE '' END  -- %3$s
   );
   -- debug   -- inspect query first
   -- RAISE NOTICE '%', _sql;
   -- execute -- unquote when tested ok
   RETURN QUERY EXECUTE _sql
   USING  _where_name;   -- $1
END
$func$;
Call:
SELECT * FROM f_demo();
SELECT * FROM f_demo('sum', TRUE, '%2');    
SELECT * FROM f_demo('avg', FALSE);
SELECT * FROM f_demo(_where_name := '%1_'); -- named param
fiddle
Old sqlfiddle
- You need a firm understanding of PL/pgSQL. Else, there is too much to explain. You'll find related answers here on SO under plpgsql for every detail in the answer. 
- All parameters are treated safely, no SQL injection possible. See: 
- Note in particular, how a - WHEREclause is added conditionally when- _where_nameis passed, with the positional parameter- $1in the query sting. The value is passed to- EXECUTEas value with the- USINGclause. No type conversion, no escaping, no chance for SQL injection. Examples:
 
- Use - DEFAULTvalues for function parameters, so you are free to provide any or none. More:
 
- The function - format()is instrumental for building complex dynamic SQL strings in a safe and clean fashion.