Given a known power supply, what are safe ranges for the volts/amps/ohms of connected components?
If a device is rated to operate from a 5 volt power supply, you need a 5 volt (+/-10% or so) power supply to operate it.  The current rating of the supply must be at least as much as the total current rating of all loads.  The loads will only draw the current they require, so there is no problem connecting a load wanting 500 mA to a supply capable of delivering 2 amps.

LEDs are a special case, and do require a current-limiting resistor.  Unlike most devices, the voltage across an operating LED is determined primarily by its chemistry and colour, and varies only slightly with applied voltage.