How big will it grow??

Quarter Horses can easily go well over 16h especially if there is TB in their immediate background.

They can also be easily well under 15 hands especially cutting horses Smart Little Lena is the #1 cutting sire in history and stands 13.3. Theres never been a NCHA Open World Champion over 15 hands.

Of course they can. You really can't generalize QHs sizes, anymore. ;)
Usually, babies seem to turn out like one parent, or the other--and not really 'inbetween', which some people hope for. They do not usually take after their sires, since that's kind of impossible... genes are a 50/50 deal. :)

Who knows lol

Your best bet is measuring the foal when its born. A foal is usually 60% of its adult height at birth ;)

^^^^said right^^^^^

Who knows. You tend to like to assume that they are going to finish around the parent's height but it is proven over and over again that it not always the case. I know of a few people who I know bought a horse expecting it to be 17+ and never made it passed the 16hh mark. Others I know were expected to be around the 16hh mark and finished nearly 18hh. Happens all the time with ponies. You can only guess.