Pruébelo así, no tengo un esquema para probarlo yo mismo, pero siento que debería funcionar (o algo así)
SELECT * FROM questions, connections
LEFT JOIN answers ON (questions.id = answers.id AND
connections.username2 = answers.username)
where connections.username1 = 'mikha';
eventualmente así
SELECT * FROM questions
LEFT JOIN answers ON (questions.id = answers.id)
LEFT JOIN connections ON (connections.username2 = answers.username)
where connections.username1 = 'mikha';
EDITAR:Encontré esto en la documentación
Así que para su caso puede ser
SELECT * FROM questions
LEFT JOIN connections
LEFT JOIN answers ON (connections.username1 = 'mikha' AND questions.id = answers.id AND
connections.username2 = answers.username)