What is the halacha if I am at the Kotel or in Geula and there are many people collecting money, am I obligated to give each one? Does it make a difference if they specifically ask me or if they just hold out their hand ?
If you were to give each one, you would have no money left!
This is not the classic case of somebody “asking you for charity” (where there is a concrete prohibition of not closing your hand), since the collectors are turning to the public in general, and not to you in particular. Of course, there is no expectation that a single individual will cater for all of the poor in Geulah or at the Kotel. See a similar concept in the Rema, Yoreh De’ah 250:1.
Another point is that we don’t know who is genuine and who isn’t, which also means that there is no concrete obligation (see Yoreh De’ah 251:10).
You can therefore choose who you want to give to, and you don’t need to give each and every collector whom you meet.