Nose dives can be tricky to deal with. Taking off late usually insures a nose dive for me, so I like to try standing up as soon as I can. You also might try starting closer to the shoulder of the wave where it isn't that steep. I've also heard starting with the board pointed in the direction you want to go helps, but I haven't got a chance to try it yet.
For duckdiving, try here :
Duckdiving is almost like "see sawing" the board under the wave. I've learned a couple things on my own you might can try. On the paddle out, position yourself farther forward on your board. Not so close to the nose that it sinks, but not much farther away. This will help you sink the nose easier when you go to dive. All you should have to do is lean forward and push to get the board to sink. When you paddle towards a breaking wave you can sometimes feel it pulling you to it. You may be tempted to slow down to avoid getting hit, but instead paddle harder straight for it. This will give you extra momentum to keep the wave from pushing you back very much. Do a duckdive just before it gets to you. If you got under the wave good enough you should have lost little ground. Even if your duck dive isn't a great one, getting your upper half under water and holding the board tightly helps a lot. After the wave passes quickly resume paddling to gain some ground.
Hope this helps,