it's small enough, but it is sort of polar. I read somewhere that urea diffuses through the membrane without the help of a transport protein. is that accurate?
It shouldn't be able to diffuse through the membrane. For example, in the nephron, urea can be reabsorbed from the collecting duct in the presence of ADH but not via diffusion through the membrane. A transporter must be present; otherwise, urea reabsorption wouldn't be regulated since it would passively diffuse through the membrane all the time depending on the concentration gradient (which is high in the collecting duct and low in the interstitial fluid).
Yea, it's not active transport. The concentration in the collecting duct is much higher than it is in the interstitial fluid and urea travels from the collecting duct into the interstitial fluid in the presence of ADH. ATP is not required because there's no transport against the gradient.