I have the following LEDs but I’m unsure how to set them up (never installed lights before). I’ll be using quite a few LEDs soldered in parallel into three strings. Two strings will have about 10 LEDs each, and the third about 20. I was going to use the following resistance calculator, http://www.hebeiltd.com.cn/?p=zz.led...tor.calculator but I don’t know what number should I use for a voltage drop across each LED and what my “desired LED current” should be.

1. Can the three strings of LEDs be configured to run off one battery?
2. Can I use a 7.2V, 3,000 mah nimh battery I already have? The battery will power only the LEDs

LED data:
Size: 3mm
Forward Voltage: 5 ~ 7V/DC
MINIMUM MCD: 12000 - 14000 MCD

Thank you

They don't sound like any bare standard LEDs that I have ever come across (normal Vf starts about 1.9v and doesn't go much higher unless they are white ones). From the voltage range given, it sounds like they have a built-in current limiter effective for just that voltage range, and so will need some extra regulation, use diagram 3 in the link. If you have a 6 volt battery, use that to measure the current on one, you then have the numbers to put into the calculator.
Remember LEDs are polarity sensitive, connect them the wrong way round, they protest by dying instantly. If that information is all that the seller is offering, it is only half the story, the important stuff having been missed. If they each pull about, say, 25mA, 40 will pull about 1A, so about a 3 hour shine with them all lit at the same time.

I got ahead of myself and didn't look at the LEDs closely - they already have a resister on the anode wire. Does mean they're ready to "go". How would the pre-installed resistor impact 10 of these LEDs in parallel/series?

From the numbers given, they are intended for a nominal 6 volt supply. You could wire as many as you like in parallel, only problem being getting them the right way round. Running them on a higher voltage requires something to limit the current into the parallel array to result in 6 volts presented to the array. Once you know the current of the total, you can just use Ohm's law to work out the value of the resistor. (Battery voltage - 6 volts, divide by the current in Amps, answer in Ohms). Once you know the voltage dropped across the resistor and the current through it, you know the power rating it needs.
You could also use a voltage regulator chip. LM7805 gives 5 volts at 1A, if that's not bright enough, there are adjustable types.