You'd have to get access to their source code to know for certain, but they almost certainly run multiple instances of custom designed nodes that index the transactions as they are seen on the network and add them to a custom relational database.
That depends on what you mean by "all" the transactions. They certainly have all the transactions that are confirmed in the blockchain. They also have MANY of the transactions that have been broadcast on the network, but which aren't yet confirmed into any blocks.
How do they get all the transactions?
You'd have to get access to their source code to know for certain, but they almost certainly run multiple instances of custom designed nodes that index the transactions as they are seen on the network and add them to a custom relational database.
Cronjob? I doubt it. That would be very inefficient, and too slow. Far more likely they have multiple daemons that run continuously and add the transactions to their DB as soon as they see it broadcast on the network.
If you don't use the wallet much, that should work.
Correct.