I think the four brothers are
The letters b, d, p and q
The positions in the competition represent
The respective positions of the letters in the alphabet
The hands and legs refer to
The lines extending from the circle in the lower case letters above and below the lines. The extensions upwards on the b and d are referred to as "hands" while downwards on the p and q are referred to as "legs".
I can defeat my brother only as I have double power than him, this will be evident from the fact when we will grow up 10 years older." The 2nd brother hesitates and says, "Actually, he is correct. But our heights will be the same".
This refers to the capitalisation of B and D. B has double the bumps but both letters are the same height.
I think GirlFriends refer to
Adjacent vowels. b has a, d has e (the most popular) and p has o but q doesn't have one.
it doesn't matter why you are asking about our racing, you can compare with our other works. I am a good traveller, and so I can arrive at any place whoever asks me to go to
This line I'm unsure about but it could be that P represents "Parking" and so you see it a lot travelling or it could simply be that p is the first letter of place.
As suggested by Stiv, it could be that the letter p can appear at the beginning middle or end of various words, unlike q.