If my opponent has a Bomat Courier and I cast an Oblivion Sower do I get to take lands from the face-down exiled cards and put them onto the battlefield? That would mean that I get to see what other cards have been exiled face-down as well.
You can't look at the face-down cards much less put any of them on the battlefield with Oblivion Sower.
From Oblivion Sower's rulings: 8/25/2015 Cards that are face down in exile have no characteristics. Such cards can’t be put onto the battlefield with Oblivion Sower’s ability.
EDIT:
I found the rule the ruling is based on: 406.3. Exiled cards are, by default, kept face up and may be examined by any player at any time. Cards "exiled face down" can't be examined by any player except when instructions allow it. However, once a player is allowed to look at a card exiled face down, that player may continue to look at that card as long as it remains exiled, even if the instruction allowing the player to do so no longer applies. A card exiled face down has no characteristics, but the spell or ability that exiled it may allow it to be played from exile. Unless that card is being cast face down (see rule 707.4), the card is turned face up just before the player announces that he or she is playing the card (see rule 601.2).
About characteristics: 109.3. An object's characteristics are name, mana cost, color, color indicator, card type, subtype, supertype, rules text, abilities, power, toughness, loyalty, hand modifier, and life modifier. Objects can have some or all of these characteristics. Any other information about an object isn't a characteristic. For example, characteristics don't include whether a permanent is tapped, a spell's target, an object's owner or controller, what an Aura enchants, and so on.
From Oblivion Sower's rulings:
8/25/2015 Cards that are face down in exile have no characteristics. Such cards can’t be put onto the battlefield with Oblivion Sower’s ability.
EDIT:
I found the rule the ruling is based on:
406.3. Exiled cards are, by default, kept face up and may be examined by any player at any time. Cards "exiled face down" can't be examined by any player except when instructions allow it. However, once a player is allowed to look at a card exiled face down, that player may continue to look at that card as long as it remains exiled, even if the instruction allowing the player to do so no longer applies. A card exiled face down has no characteristics, but the spell or ability that exiled it may allow it to be played from exile. Unless that card is being cast face down (see rule 707.4), the card is turned face up just before the player announces that he or she is playing the card (see rule 601.2).
About characteristics:
109.3. An object's characteristics are name, mana cost, color, color indicator, card type, subtype, supertype, rules text, abilities, power, toughness, loyalty, hand modifier, and life modifier. Objects can have some or all of these characteristics. Any other information about an object isn't a characteristic. For example, characteristics don't include whether a permanent is tapped, a spell's target, an object's owner or controller, what an Aura enchants, and so on.