The link below spells out the specifications for USB. Your situation is the charging port type of connection. Basically it just needs a nominal 5V at currents as much as 1.5A, though there is no real upper limit except voltage drops and connector rating. At this point the current limits and the voltage is reduced.
Thus you have a 5V regulator rated at 1A that can deliver up to 1.5A then current becomes limited. It will also shut down if it becomes too hot (as it dissipates power according to voltage dropped across it and current drawn. My mobile phone charger is 5V @ 700mA. It should not matter if it has more current rating, as the phone presumably limits the current itself, but there is no certainty of this..
You would certainly need a heat-sink. The TO220 package can dissipate about 2W in free air.
If you have 11.1V or more from the battery, and 500mA for an example, the power is:
(11.1V - 5V) * 0.5A = 3W.
The heat-sink etc is de-rated in an enclosed box.
Not sure why you have 3 * 5V regulators, presumably there are 3 ports. Make sure the battery can work safely with the maximum current. Look up battery rating for maximum continuous current. The battery can overheat with dire consequences, especially as it will be at a high ambient due to the heat-sink in the box. One solution is a small fan. Another is careful design of the box and heat-sink arrangement. The power dissipated inside the box can be reduced a little by using a switch mode regulator instead assuming it has a higher efficiency.
Make sure there is a fuse fitted in series with the battery that is rated at the battery maximum 6A current or less, and that wires are appropriate sizes for the current. If there is a battery switch (there should be) make sure it is rated the same way for current. Choose 2A hookup wire to suit each port, but bigger 6A or 10A where 3 ports are shared and running to the regulators. A short circuit with this battery is a hazard, so must be properly considered. It can deliver 128A, so explosion and fire hazard with a short circuit.
Look up data sheets for your regulator device and the battery. Note the maximum temperature 45°C. This is where plastic seals etc start to soften.
The second link shows some data for what might be your battery.
The third link shows precautions for LiPo battery packs. You might want to consider a low voltage cutout that disconnects the battery if it is below 10.1 - 10.5V. Use a proper charger for this battery. Note the disposal information.
Also note the capacity say 3500mAh means that for 500mA load it will run 6h but for 3A only 1h or so. This is considering the low voltage cutout.
The fourth link shows a low voltage cutout but will need the values for the 3 resistors to be worked out. Look up the LM10 data sheet. It has a bulit in reference voltage for this. Otherwise look up other circuits.