Queen and pawn vs queen endings

Question 1 is it a draw if the king is in front

Good luck.

http://www.shredderchess.com/online-chess/online-databases/endgame-database.html

You can put there(the link) every endgame with 6 or less pieces(including kings) and because queen+pawn+king vs king and queen are 5 pieces, you can put every endgame of that kind and see if they are wins or draws.

There are some queen and pawn vs queen endgames in Averbach's endgame book and I think that there are few of them in some encyclopedias of endgames like L. Polgar's book "Chess Endgames".

I recently had this ending practice in a real game.

It depends on the position, of course, but normally, Q + p always wins against Q. There are some conditions apply.
Suppose, you are the weaker side and fight for a draw. The closer your king is to the pawn - the better, as ideally you want to swap queens while taking the pawn, or you want to swap queens with a draw in the K +P vs K ending. 
If you are the stronger side, then you need to cut off the enemy's king threatening the queen exchange with a check and going to a winning pawn ending. Or you want to promote another queen moving your pawn with support of K & Q. It is very easy to combine the pawn advance and escaping from queen checks.

Theoretically I doubt one can say that Q+P generally wins against Q as there are way too many exceptions. I believe it is true though for most of these endings occurring in actual chess games. The main reason for it is that the plus pawn is mostly a passed pawn created away from the opposing king. While the king would be most powerful in front of that pawn in the Q+P vs Q ending, it is forced to stay away to cover up weaknesses elsewhere on the board in the preceding game phase. Therefore the king ends up being cut off by the time the other material has been eliminated.

This is why the R+P vs R ending is a draw much more often in actual chess games. The opposing king need not fear the rook as much as a queen and will not hesitate to block the passed pawn when the opportunity arises.

These are notes aside from the question of whether the players actually get the most out of these endings. Having a won endgame is one thing, winning it is quite another.

Not necessarily. The position below is a draw with Black to play (also with White to play). But if the black king were on e6 or e7 or e8, Black to play would be losing.

Black to play and draw

That's another important principle of this ending. It is best for the black king to be in front of the pawn (on or about the same file) but if such is not feasible, then the king should stay away as far as possible. n9531l's diagram is typical in that respect. The whole endgame is about (avoiding) queen exchanges enforced by nasty checks. If the black king could step outside the chessboard for a while, it would be impossible to promote the pawn in almost any Q+P vs Q ending.