When a wand chooses the wizard - it does not mean that the wand can be used only by that wizard. It means that both the wand's ability and the wizard's ability are at their maximum when the wizard uses the wand. We can clearly see that Harry uses Hermione's, then Draco's wand in the Deathly Hallows. When Hermione's wand also works for him - he feels most comfortable with Draco's wand as that wand had switched its allegiance.
Harry: “A person can still use a wand that hasn’t chosen them, though?”
Ollivander: “Oh yes, if you are any wizard at all you will be able to channel your magic through almost any instrument. The best results, however, must always come where there is the strongest affinity between wizard and wand. These connections are complex. An initial attraction, and then a mutual quest for experience, the wand learning from the wizard, the wizard from the wand.”
Can a wizard be chosen by two wands?
Edited: In the Sorcerer's stone - Ollivander tells Harry:
"You have your mother's eyes. It seems only yesterday she was in here herself, buying her first wand."
-- Harry Potter and the Sorcerer's Stone, CHapter 5: Diagon Alley.
Note that he says her FIRST wand. That indicates Lily had more than one - and she had come to Ollivander more than once. SO yes - I think a wizard can be chosen by more than one wand - since people who have broken their wands have had them replaced; people who win the Elder wand also have their allegiances changed from their previous wand. According to Ollivander in the Deathly Hallows - this is true of all wands which are won.
Ollivander: “Perhaps not. If you took it –”
Harry: “—I did – ”
Ollivander: “—then it may be yours. Of course, the manner of taking
matters. Much also depends upon the wand itself.In general, however,
where a wand has been won, its allegiance will change.”
Can 2 or more persons be chosen by a single wand?
Again - I think this should be possible - given the fact that Harry, Draco and Voldemort were able to use multiple wands. If they have similar qualities - then the wand maybe able to perform reasonably well. But if they are different in nature - maybe the wand will not perform to its fullest capability. Furthermore - if there was a chance that wands need to be custom made for a wizard - I think wand makers will operate more like tailors than like clothing outlets! It seems unlikely that they will store multiple wands - if the wands did not have the ability to choose more than 1 person in the world.
What if the wandmaker hasn't created that particular wand by that time that would choose him?
I remember Ollivander taking Harry's measurements when searching for a wand. I also remember Ollivander making a wand specially for Luna in the Deathly Hallows. So my inference is - the wand maker will make a wand specially for the person in question. What that depends on is difficult to say - since at age 11 - Ollivander would have had no idea about Harry's qualities or temperament.
If the wandmaker makes a wand specifically for a child, how can he be sure that the wand would choose him/her at all?
I don't think there is any support for a wand having been made specifically for a child. Ollivander made a wand specifically for Luna in the Deathly Hallows - but since he spent a lot of time with her in the Malfoy Mansion and in Shell Cottage - he has a pretty clear idea about her qualities and temperament.
According to Ollivander - the wand and the wizard are connected by a complex connection - starting with initial attraction and then a mutual quest for experience - learning from one another. So - if a child's nature is known - which should be the case since the wand is being made for the child - it is highly possible that even though the child may not be able to exploit the full power of the wand - they would eventually grow - learning from each other. Of course - since there is no support of such a wand ever being made - I can only guess at this point.
