Wow! Worthy of a college lecture. Thank you for taking the time to write such an educational article. I've learned a lot, including how much I've done "wrong" for years. You truly are a plant guru.1) Doesn't really matter, but preferably less than 12 inches (30 cm) in depth from the light to the substrate, unless you are using a high grade light such as an ONF or Twinstar. Tall or narrow tanks are more difficult to light properly, as the lighting needs to be more powerful or you need to stack more substrate, which means spending more money.
2) They are slow growing, but probably Marsilea crenata or Marsilea hirsuta, both usually sold as "four-leaf clover". These tolerate lower light levels and less CO2 than most other carpeting plants. In my experience dwarf hairgrasses are also easy but unfortunately do not transition from a dry-start very well. Staurogyne repens is also easy.
It is usually used as a stem plant, but pearlweed (Micranthemum micranthemoides) forms a nice, easy, fast-growing carpet under good lighting and injected CO2, as does shade mudflower (Micranthemum umbrosum).
3) I have a carpet of dwarf baby tears in my 2 gallon (8 liter) tank, the floor plan is only 8" x 8" (20cm x 20cm). I am also currently dry-starting glosso in my 4 gallon (16 liter) which is 10" x 10" (25cm x 25cm). Provided you meet their needs for light, water, nutrients, and CO2, you can grow them in anything, even a small vase or bowl (look up Wabi-Kusa and Kokedama).