Can I insert a carbon seatpost up to 20cm deep into seat tube? The seattube is carbon as well. Total length of the seatpost is 35cm. The shape of the seatpost is aero seatpost (tear drop shape). It's a Pinarello Dogma.
On most frames, yes, you can put as much of the post into the frame as you'd like. However, you are likely to remove graphics, and scratch the top coat of the carbon, so if you care about things like that, don't put it farther into the frame than is necessary.
If it is a permanent position, cut it, as suggested above. Be sure to check the manufacturers' recommendations for your post. Not every post can be cut to any length.
If you need to, try to put it at that position, gently. If anything stops, sticks, blocks it, or doesn't feel right, stop.
Sure you could, Only the top two or three inches of the seat tube are machined to match the diameter of the seatpost. But my question is why you'd want to do so. Cut the seatpost off!! You don't need more than about 4 - 5 inches inside the frame. Put a fine-tooth blade in your hacksaw, wrap some good tape just above where you are going to cut it, clamp the part you're cutting off in a vise, and saw away--gently--don't press down too hard on the saw. It'll turn out just fine.