1.
In order for a reed switch to be most sensitive to the magnet, they must be oriented in a particular direction relative to each other. (It is the same with a hall sensor.) You might find a way to arrange two reed switches in parallel, so that one or the other will operate. (Or two hall sensors.)
You will probably need to amplify the sensor output, so that it can trigger another amplifying device.
Or instead of a hall sensor, there is such a thing as a hall switch, if you can manage to locate one which is sensitive enough to use by itself.
Neodymium magnets are strong for their size. You can stack several of them, in order to increase their attraction at a distance.
2.
As far as wireless detection...
It could work to have an oscillator broadcast a brief carrier wave every 5-10 seconds. The second circuit is tuned to detect that frequency and amplify it, to turn on the led.
Both the transmitter and receiver can be very small and very simple, powered by coin cells. If you leave them running long term, then it is hard to predict how long the batteries will last.