1. The flickering is expected because LEDs are diodes so they block half of the AC cycles. Since AC is usually at 50 to 60Hz, this halves the frequency to 25 to 30Hz, which is a frequency that our eyes become sensitive to.
There are a couple of different ways to address this issue. One is to use a rectifier to convert the AC into DC. It can be done by either a half-wave rectifier or full-wave rectifier, and adding a capacitor after the rectifier will serve the purpose of smoothing out the voltage so it will effectively become DC, eliminating the flickering. You can also use some other type of AC to DC converters, though anything other than a simple rectifier would increase the cost pretty significantly. Finally, you can also use OpenSprinkler to control relays, and the relays in turn control LEDs through a DC power source. This again will be bulky and likely expensive, so not as elegant as having the controller directly interface with LEDs.
2. You can connect a multi-meter in series on the common (COM) wire to measure AC current. LEDs are generally pretty power efficient so unless if you are worried that it’s exceeding 800mA per zone, it shouldn’t be a problem for the triac on OpenSprinkler.
3. Length of the cable usually affects the wire resistance. The longer the wire, the higher the resistance and the more power wasted on the wire. Technically both the length and wire gauge (AWG) affect the resistance, that’s why if you plan to run longer wires usually you would want to also increase the thickness to counteract the increased resistance due to wire length. In your particular case, though,. it probably doesn’t matter that much as the current draw of the LEDs is very small, so the resistance won’t end up eating the power as significantly as in other cases.
In the end, if you are using OpenSprinkler to purely control LEDs, I would recommend considering the DC-powered OpenSprinkler since it outputs DC voltage.