1. Would this 7.5Gal cube be big enough to support one of these little eco systems?
Yeah, that would be fine. I have a planted 5 gallon and it is working very well. I'd just look to see how tall the plants get. Is the light florescent? That's what you need for plants. If not, get low-light hardy plants and place the tank where there is natural light. I have an incandescent for mine, but all plants are low light and lots of sunlight in the room, and they are doing very well.
2. What would you all recommend for my grass-like plant to take hold of the substrate? Is one kind easier for beginners? I want a carpeting effect.
I agree with the java moss idea. That or I think dwarf hairgrass is a good one too.
3. Do you all have luck with getting plants in the mail?
I got plants from http://www.shop.plantedaquariumscentral.com/main.sc
Highly recommended! Great selection and plants came in wonderful condition. They were packages very well. No hitchhikers. And she threw in a few extra plants. Shipping is a little expensive, but very worth it! The site also tell you what lighting conditions each plant needs, how hardy they are, how tall they get, etc.
4. Anyone have tips on driftwood?
I get the same stuff. Some pieces of driftwood will leak tannins for years. Water changes lighten the water again. I don't think the darker water looks too bad. As for the white stuff, I got it too. In my tank and my dads. I have found that my mystery snail loves the stuff. And during water changes, I take it out, rinse it, and scrub it off. Both tanks now don't have the white stuff. Maybe it goes away after time?
5. Do I need a filter?
Yeah, you need a filter. It introduced air to the water and keeps water moving a bit. I think most plants need one.