No. It is never safe to let your baby sleep unattended on the couch. The baby may roll off unexpectedly, and the couch is usually soft which is a risk factor for sids (if baby turns prone). In addition, baby should never sleep on the couch with an adult, because this has been shown to be a significant risk factor for sids. The couch, while comfortable for an adult nap, is not a safe place for baby.
No. Be careful that your baby doesn't roll off the couch, there are no side rails.
No. Young babies should not sleep on a couch, nor on an adult bed. Neither are as safe as a baby bassinet or baby crib. If sleeping on a couch, a baby can fall off the couch, can get stuck between the couch cushions, or have some other unforeseen bad thing happen.