Unlike other creature types in Magic that are each only one word, the two words "Time Lord" represent a single creature subtype. Time Lord is the only two-word creature type.

If an effect instructs you to choose a creature type, you may choose Time Lord.

Drawing cards from the bottom of your library is exactly the same as drawing from the top, except that you take the bottom card of your library and put it into your hand.

Neither "Time" nor "Lord" are creature types. Some older cards were printed with the subtype "Lord," but all of those cards have updated Oracle card text that removed that type.

River Song's first ability applies to all cards you draw while it is on the battlefield, not just the card you draw for your turn.