-ra is part of the group -ra/-on/-ról which deals with the surface of an object, usually the upper one. If we take the table as an example, az asztalra means something gets put onto the table; then it will be az asztalon, on the table; and then it may move az asztalról, from the table, leaving its surface.
The group -hoz/-nál/-tól has the same relationship, but this time it's about the surrounding of the object. Let's look at the table again: az asztalhoz means you're moving to the table; then you're az asztalnál, at the table; and if you move away again, you say az asztaltól, away from the table.
The difference between "at" and "by" the table (both translated as az asztalnál) is a bit subtle in English. To be "at" an object usually means you're doing something with it. If you're at the door, you're waiting for someone to open it. If you're at the bus stop, you're waiting for the bus to come. If you're at the table, you make use of it for eating or reading the newspaper. You fish at a lake, look at the mirror, or buy groceries at a store.
"By" carries a meaning of coincidence, that the object in question is just closeby, but you don't interact with it. If you're standing by a bus stop, you're not actually waiting for the bus. You can look at the sunset by the sea. Trees stand by the house, people pass by a store.
Basically it's a matter of interaction (at) versus surrounding (by).
No, that has a different meaning. Hol is translated with "where" and is referring to a single place, not a direction. So if you ask "Hol siettek?" - "Where are you hurrying?" you might get an answer like "Az áruházban" - "In the department store". That's not what you want here. You want to know which object they are moving to.
This sentence has never been uttered by a native English speaker. "What" infers a thing, but we never hurry to a thing in English. We hurry to DO a thing. Or we hurry TO a place. So it could be "Where are you hurrying to?" or "What are you hurrying to do?" (also unnatural, but acceptable). I think the best American english translation would be "What are you hurrying off to?". I know, thats horrible grammar, but its what we say in this context.