Selecting multiple columns/fields in MySQL subquery

Yes, you can do this. The knack you need is the concept that there are two ways of getting tables out of the table server. One way is ..

FROM TABLE A

The other way is

FROM (SELECT col as name1, col2 as name2 FROM ...) B

Notice that the select clause and the parentheses around it are a table, a virtual table.

So, using your second code example (I am guessing at the columns you are hoping to retrieve here):

SELECT a.attr, b.id, b.trans, b.lang
FROM attribute a
JOIN (
 SELECT at.id AS id, at.translation AS trans, at.language AS lang, a.attribute
 FROM attributeTranslation at
) b ON (a.id = b.attribute AND b.lang = 1)

Notice that your real table attribute is the first table in this join, and that this virtual table I've called b is the second table.

This technique comes in especially handy when the virtual table is a summary table of some kind. e.g.

SELECT a.attr, b.id, b.trans, b.lang, c.langcount
FROM attribute a
JOIN (
 SELECT at.id AS id, at.translation AS trans, at.language AS lang, at.attribute
 FROM attributeTranslation at
) b ON (a.id = b.attribute AND b.lang = 1)
JOIN (
 SELECT count(*) AS langcount,  at.attribute
 FROM attributeTranslation at
 GROUP BY at.attribute
) c ON (a.id = c.attribute)

See how that goes? You've generated a virtual table c containing two columns, joined it to the other two, used one of the columns for the ON clause, and returned the other as a column in your result set.