The state of Imladris during the War of the Ring

[Falagar]

Since no attack on Imladris is mentioned anywhere (and the attacks on Lórien, Dale and Erebor are) I don't believe there was any. Sauron probably thought he had everything under control, the attack on Lórien was (if my memory serves me right) only to prevent Galadriel and Celeborn from sending Gondor help, and when he had beaten Minas Tirith/Gondor conquring the rest was a small problem (in his eyes).

Secondly, how? Sauron cannot send a large army to Rivendell: Gondor blocks the south passage, while Erebor and Dale blocks the northern one. Sure, he could send forces over the middle portion of the Anduin, but I'm sure the residents of Rivendell could handle them.

The same way as Lórien: from Dol Guldur. Or perhaps from Moria or Gundabad (both which Sauron probably had at least some control over).