Okay sorry for the long convoluted post everyone i haven't posted in a while and see quite a bit of confusion on both the poster's questions (not just on this thread, but all over). Any one who wants to can just skip to the bottom and find my generalization. I even highlighted it for really lazy people like me!
First thing first, the watts/gal rule. I guess the most important thing to know about it is that it's wrong. Well, I mean it can be a decent guideline, but doesn't work in a number of scenarios. For starters it's fails on small tanks. As you noted 3 watts would not grow any plant in any size tank no matter how small. The second thing is watts/gal does not address the lighting type or efficiency of the reflector, nor does it measure how much water the light has to travel through in order to get to the recipient. Some examples here: 60 watts of incandescent light is next to nothing for plants, because incandescent bulbs have terrible efficiency, as anyone knows who has tried to take one out of the socket while on and gotten burned, they produce mostly heat, not light. On the other end of the spectrum T-5 HO lights are very efficient, and therefore run cool and produce far more intense light for the same wattage. Regular florescent and PC or CFL lights fall in between these two.
What you are after for photosynthesis is lux, pluralized as lumens. This is how much light is actually getting to your plants. Several factors influence this number including lighting type, wattage, distance from source to aquarium, reflector efficiency, transparency of hoods/covers, depth of water, plants/objects in the way, and so on. If you don't care about any of this sorry for the rambling, just take away from it that if you are using a less efficient light source, or placing it farther away, or
Now on to the second question. The plants you mentioned require a moderate to high amount of lighting. In a 20L you are going to want at least 2 watts/gal even using T5HO lighting. Other types are going to require probably 3 plus. Another reason you'll need this much light is because these plants are on the bottom of the tank and therefore light has to travel further through the water.
Here comes the problem. When you add more light you are going to increase the growth of algae. Now algae isn't really a huge problem in a fish only tank (unless completely out of control) because it isn't harmful to fish and really the only problem is the ugly nature of everything being green or brown. In a planted tank however, algae uses the same nutrients plants do and can lead to the plants suffering nutrient deficiency. Usually this takes the form of yellowing/browning and dying leaves, and eventually growth will probably come to a crawl or stop altogether. This tank is out of balance.
The only way to really fight this phenomena is to allow the plants to grow at such a rate that they are using the nutrients which previously were in control of the algae. Fast growing plants such as Vals, Anachris, Hornwort, and various kinds of hygro are great for this, as they are real nutrient hogs. In order for plants to grow quickly in high light environments they must have enough nutrients. I don't want to go overboard here because certainly there could be a 20 page discussion on all the various nutrients plants need.
CO2 is necessary in this scenario because it is one of the main ingredients plants need to survive. Having sufficient CO2 for all your plants is necessary for them to outgrow algae and be healthy, lush and green. This is when heavily planted tanks will need more CO2 than tanks with less plants in them. Of course there is some amount of CO2 always present in fish tanks because for two reasons:
1) The atmosphere contains a level of CO2, therefore so does your fish tank. Surface agitation increases the gas exchange between your tank and the atmosphere.
2) Nitrification: The bacteria that converts fish waste from ammonia to nitrite to nitrate produces an amount of CO2 also. An additional benefit is the nitrate produced is also used by your plants in the form of Nitrogen. (isn't nature amazing??)
Where supplemental CO2 comes into play is when you have a lot of light and therefore need to outpace the algae growth and keep your plants growing healthy. This is also true because many common aquarium plants are not found completely submersed in nature and therefore have more CO2 (not to mention light) available to them. Of course CO2 is not the only nutrient required to maintain healthy growing plants, a good regimen of macro/micro nutrients would also be needed. But since you didn't really ask about that part, I won't go into great detail.
So basically the really long, winding road type answer to your question is:
In order to grow those plants you wish to grow to look like a carpet on the bottom of your aquarium you will need a good amount of quality lighting 2-4 wpg in the daylight (5500-6700K) spectrum, and some type of supplemental co2 and fertilization routine.
I know it sounds like a lot but there are ways you can cut down the amount of cost especially in a smaller tank using techniques like DIY CO2, and cheaper lighting which can be found at any lowes/home depot/walmart, etc. Also there's the other possibility of doing a low light/tech plant which can be awesome you just have to be aware there are some plants that will just never thrive in there.
Good luck with whatever happens, and try not to get too frustrated. Mistakes are definitely what improved my understanding and evolution of my tanks (if not my wallet thickness!!!)
