Your rabbit looks like it is part lionhead.
No it is not 2-3 weeks old. A 2 week old bunny is just starting to open its eyes and three weeks is still drinking from mom but has lots of baby bunny characteristics which yours doesnt. Its body is longer and hair is long as well. Id guess the age at about 4-6 weeks of age. You can start offering pellets but since you have been giving milk you shouldnt completely stop. Also offer plenty of hay (timothy would be fine unless the pellets you are feeding dont hve alfalfa in them. If your pellets are timothy based then give alfalfa hay.
Also you can sex at any time. I even try at day 1 and am not doing too bad at sex determination. I double check when they are two weeks and then again at 4-5 weeks just to make sure. It all depends on how experienced you are