Effect of LEDs in series instead of parallel with resistors

Using only one resistor for 6 LEDs is not a good idea: if there's a slight difference in forward voltage between two LEDs one will light brighter than the other one.

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Splitting the 6 LEDs in two groups of 3 and using additional inputs of the ULN2803A would only help if you would exceed the maximum current for one driver. But each driver of the ULN2803A can sink 500 mA, while 6 LEDs will need only 120 mA.

The torches are apparently relying on the internal resistance of the LEDs and the battery to limit the current. Typical voltage drop across a single LED junction itself is usually less than 1.5V, but I've seen "single" LEDs that have a number of individual diodes inside to make up a given voltage drop, which may be what is going on.

Without measuring, it is difficult to guess the current drawn when the LEDs will be connected to your 5V supply, Typically I run them with at least 10-20 mA to light them up to a decent brightness.

As for a transistor, any mosfet with a "logic level" gate drive that can handle enough current would be suitable. One example is AOT460, which turns on when the voltage applied from gate to source is +2.2V or more. Cost $1.63 At Digikey, I would buy a few just in case.

Or search Digikey for "FETs - Single" then restrict the results based on Vgs. Make sure the "drain to source voltage" is sufficient, as well as . The power dissipated in the mosfet will be (Rdson)*I^2, but I expect any of the ones that have a few mOhm for Rdson will not heat up too much. When you search make sure to click the "in stock" check box.