The following answwrs are from personal experience and observation of profession hobbyists who grow aquarium plants for profit
1. could I just weigh down the plants with something, (not the floating ones) or do I have to do soil capped with gravel?
I wouldn't recommend soil for this setup. as it can become very messy with constant uprooting.
I actually would recommend red floramax or flourite.
2. Do I have to filter the tanks, or will a simple air stone or two work? (I've personally found that my water sprite does well with a HOB filter)
An airstone will work just fine, I petsonally prefer filters as airstones are noisy...
to be honest you dont need either of these
3. How about lighting? Can I just use big incandescent lighting strips and a plexiglass lid? (I have loads of the lighting strips, they hang from chains)
use flourescent or professional LEDs. compact flourescent works quite well. you can also look into led flood lights from ebay... what you need is lighting around the 6500k range
4. Should I heat the tanks? How about fertilizer?
heatin isnt absolutely neccessary neccessary... plants prefer cooler temperatures... around 70F is a good temp.
I would recommend stocking the tanks. to make it simple, you can just do snail. as long as you feed the snails... there will be ferts.
if you dont like snails i will opt for a cold water feeder minnow...
5. Can I put snails in? I've heard some of them eat the plants. I have some pond snails, and two ramshorns. I have had the ramshorns since December, and they haven't bred. I'm starting to think that they're both the same sex. My pond snails, however, are breeding like... um... snails?
ramshorns are hermaphrodites, either one can reproduce as long as they have another....partner
6. What would be a decent temp for the tanks? Does temp matter?
yes at a cooler temp plants will grow slower, but at temps too high they will stunt or die off, the low 70s is a goid temperature for growth
7. Is there a specific water level needed for each tank? Would having a low water level for floating plants work, or do they prefer high water levels?
i dont recommend floating plants for your set up...
Is there anything else I should know?
learn how to ship plants!