1.) A 20 Long tank is about 12" high. With a couple inches of substrate that's around 10 inches from your light to the substrate. According to Current's specs, the Freshwater LED [not the Freshwater LED+ right? Big difference] you'll get 15 PAR at 12" inches so you'd probably be getting around 20 PAR. That's enough to grow many low light plants but not quickly and you'll have to experiment. Taller plants will have an easier time of it but lower ground cover plants will not thrive as easily. The sword should be fine but the grasses are a bit more iffy.
Here is an explanation of PAR: https://www.plantedtank.net/forums/sh...d.php?t=184368
2.) Here is a stocking calculator that can help you with planning your bioload. http://www.aqadvisor.com/
3.) See answer to question 2 and yes small Tetras have a surprisingly low bioload.
4.) pH is really not as important as you may think. My pH here is between 8.0 and 8.4 and I've never had any problems keeping Tetras or Corys.
5.) No, getting a new filter will not disrupt the cycle so long as you run the new one in tandem with the already cycled filter for a few weeks.
6.) What are your nitrite readings?