Yes, you can move your Commander to the Command zone as part of drawing it, even if it was face-down on top of your library. It would not count as a draw; I'll cover why later in response to your question #3.
Commander-ness and location of a commander is always known at all times to all players, even in hidden zones.
Commander-ness of a card, no matter its state or location, is always known to all players. This includes when a card is face-down (such as via morph or face-down in exile) or in a hidden zone such as your hand or library. This much has been explicitly confirmed by the EDH Rules Committee. Genomancer, one of the EDH Rules Committee members, writes in 2010 in an FAQ thread on the official Commander forums:[note 1]
Long story short, the location of a General is known to all players at any time no matter which zone it's in, or whether it's face down/face up. That includes being in the library or face-down from something like Tuck+Grimoire Thief, and it means a player has the option to Command-zone their General instead of it being exiled face down.
[... further down in the summary, re-stated ...]
- The location and identity of a General is known to all players at all times, no matter what its status/effects/location.
(“General” as used here means your Commander card.[note 2])
This effectively makes a Commander card “marked” in hidden zones: you're obligated to clarify that's a Commander card if you can know, and anyone including you is entitled to find this out. This ruling of needing to know commander-ness anywhere exists to handle effects like commander damage from morphed commanders (a 2/2 face-down commander still deals commander damage) and extends to all zones for various other corner cases.
My own EDH decks have my commander sleeved in a different color to the rest: you'll know where my commander is because it'll be the only red-sleeved card in an otherwise green-sleeved deck. If you don't have your commander in a different-color sleeve, you can “bookmark” your commander before putting it in a hidden zone or turning it face-down by slipping a scrap of paper to the sleeve that'll stick out the top, helping you and others track its location and commander-ness. Genomancer recommends the uniquely colored sleeve approach.
In that quote, Genomancer confirms that even in the case of Grimoire Thief exiling a card from a player's library, that player is entitled to know whether that card was their commander and, if so, they are entitled to replace the exile with a move to the command zone.
(If you didn't bookmark your commander, you could re-identify its position in a library by searching for it in your library, noting its position relative to the top or bottom, bookmarking it then, shuffling your library, and re-inserting your commander card into the right position.)
Note 1: Wizards of the Coast acknowledges Commander as being officially managed by the EDH Rules Committee on the official MTGCommander site (mtgcommander.com
or mtgcommander.net
— same site, two aliased domains), therefore EDH Rules Committee FAQ rulings are official rulings for how Commander works even from WotC's perspective. This will be news to some, but for examples of this deferment, the Full Rules link on WotC's Commander Format page links to http://mtgcommander.com/rules.php; and in each Commander edition's release notes WotC acknowledges MTGCommander.net as being the rules source. Consistently WotC has consistently indicated no interest in taking control of the game away from the MTGCommander EDH Rules Committee.
Note 2: The format's original name was Elder Dragon Highlander, and the card you chose was called your General. When WIzards released the first official Commander supplement in 2011, they couldn't use the “Highlander” name because of legal concerns — so instead their personal branding of the format was that it was called Commander, and the card you chose was your Commander card. The terminology here is interchangeable.
Answering your specific questions
- Is the card drawn known to the player during the draw, or only after the draw?
Game rules say you should know the card you're about to draw is your Commander card, because you have perpetual total access to that information.
If your Commander card is bookmarked or in a uniquely-colored sleeve, you'll know before the draw.
Otherwise if you don't know it's your commander but you want to move your commander to the command zone, I suggest handling it like this:
- Draw the card.
- See it's your commander. EDH rules say you should have been entitled to know this before you drew the card.
- Backtrack to just before you drew it. Move your commander card back out of your hand, and reveal that it's your commander to your playgroup.
- Say you're replacing the draw with a move to the command zone.
- Move your commander from the library to the command zone.
- Subsequently, if the top card is only presumed to be the commander, but is actually not, can the player be aware of this while drawing the card?
In theory, the player is entitled to have perfect knowledge of whether that card is their commander, and if it isn't, where their commander actually is in their deck. The player can be considered to be aware of this fact when they draw the card. Backtrack to just before the draw occurs if necessary.
- Does the replacement of the destination replace the whole draw effect, or just a part of it? Is the card still drawn, even though it didn't go to the hand?
The replacement effect replaces just drawing that specific card. Per the rules on drawing a card, drawing multiple cards is treated as drawing one card multiple times:
120.2. Cards may only be drawn one at a time. If a player is instructed to draw multiple cards, that player performs that many individual card draws.
Also, replaced effects aren't considered to have happened, so if you replace a draw, the draw never happened. From the rules on replacement effects:
614.6. If an event is replaced, it never happens. A modified event occurs instead, which may in turn trigger abilities. [...]
If you draw three cards with Concentrate and one is your commander, one of two things happens (your choice of which):
- You draw two cards. One card moves from your library to the command zone.
- You draw three cards. One of those cards in your hand is your commander, and your opponents are entitled to know this is true.
- Or, in other words: At which point during the draw action does the replacement of the destination occur?
You replace it as you take the action of drawing that specific card. If you cast Concentration whilst your commander is the second from the top card in your library, you'll do the following:
- Draw a card.
- Decide whether to draw your commander card, or move it to the command zone from your library. Do this before you would draw the third card — you must make this decision without knowing what that card will be.
- Draw a card.