Ok, first I want to say that it looks like you have at least 2 if not 4 plants that are not truely aquatic. I can't really tell but a close up of the ends and the middle will help to identify them. A good description could help or you can click HERE
to try and identify them. It will tell you if they are aquatic or not.
The next thing is you are getting up to medium light for a 45 gallon so CO2 would definately benefit you. I would also recommend either a large HOB filter or a canster and they both work just fine for planted tanks. Any CO2 is always better tha non until you really get a good grasp on plants and their needs.
Your substrate should grow plants fine but needs to be a little deeper, 2-3 inches is a good range for plants as it supports the large root systems that some plants can get and also allows for more surface area for bacteria to break down the mulm and fish waste into useful nitrients for the plants. I have standard epoxy gravel and soe river gravel in mine and I can grow pretty much any plant I want to that fits my lighting.
I thikn the best piece of advice I can give is be patient. Plants will grow better in time once they have the nitrients they need and descent lighitng but it can take some time. Don't give up on it because planted tanks are very rewarding but can be very frustrating. Keep on the right track, ask lots of quesitns and you will learn to grow plants and be successful.
As for undergravel heaters, have no experience with them so I can't help there.