select from mysql table between datetime x min ago and datetime x min ago

For your first query:

SELECT username
FROM online
WHERE time > NOW() - INTERVAL 15 MINUTE

And for your second:

SELECT username
FROM online
WHERE time BETWEEN NOW() - INTERVAL 60 MINUTE AND NOW() - INTERVAL 15 MINUTE

Both these queries assume that each user only appears once in the online table (and if this is indeed the case you should add a UNIQUE constraint to enforce that).

If a username can appear more than once in the table you just need to add DISTINCT after SELECT for your first query, but you need a slightly different approach for your second query:

SELECT DISTINCT username
FROM online
WHERE time > NOW() - INTERVAL 60 MINUTE
AND NOT EXISTS
(
    SELECT *
    FROM online
    WHERE time > NOW() - INTERVAL 15 MINUTE
)