Is the Queen plus pawn versus Queen endgame always a draw? In a Queen + King versus Queen + King endgame (including zero or more pawns) these is a strong draw tendency due to the fact that a Queen can deliver multiple checks in a row to the opponents open King. My question concerns the Queen+pawn versus Queen endgame. Assuming that the pawn is on its initial square (second rank for white, seventh rank for black), are all these endgames objectively drawn? Second of all, what is the best strategy for the player with the material advantage to aim for a win?
My question concerns the Queen+pawn versus Queen endgame. Assuming that the pawn is on its initial square (second rank for white, seventh rank for black), are all these endgames objectively drawn? Second of all, what is the best strategy for the player with the material advantage to aim for a win?


Emphasis above are mine, and since you have 2 questions I shall answer both separately.


  are all these endgames objectively drawn?


No they are absolutely not!


  Second of all, what is the best strategy for the player with the material advantage to aim for a win?


Without seeing the exact position I can not answer that-your question is too broad-these endgames require thorough study as everything counts there ( the position of the kings, who moves first and so on ). 

I can recommend you Yuri Averbakh-Comprehensive Chess Endings ( Volume 3 ) to learn how to win Q+P+K vs K+Q endgames. There you have described patterns for winning with the bishop/knight/rook/central pawn, queen and king vs king and queen. 

I have just suggested the above book because it is written for all levels of play-from novice up to grandmaster-so with that knowledge you can not squander your edge, but if you find something else even better for you! 

The key is just to learn how to recognize winning position and to learn how to win it.

All you have to do now, is to use this tablebase to see how can you reach the winning position.

If you have trouble finding exact winning moves you can always go through tablebase moves-just click on the notation.

SUMMARY:

Learn how to win Q+P+K vs K+Q endgames->input the position you are interested in into tablebase->if winnable, play through moves to see how to reach winning position.

I know that this might be too broad of an answer to you, but you ask for help in Queen endgames and these are the toughest to master. Just one imprecise move ( not to mention wrong one ) gives your opponent a draw and squanders your edge! 

Hopefully this answer helped you a little.

If you have further question leave a comment and I will reply.

Best regards.