We made one from a kit from the craft store. The mold was a thin plastic so I imagine you could use an old plastic container if you wanted (something you could sacrifice as needed). I clicked on the link you share and scrolled down to the photos of the cardboard boxes - I wouldn't have thought of that but I guess the cement hardens fast enough that the water doesn't soak into it. I did notice in the photo that some of the boxes are misshapen - so I would think you would have to worry about the weight of the cement pushing the sides out.
We made ours in 2010 and it has survived quite a few winters outside. I have not seen any change in color, and no cracks or discoloration. We don't walk on it so I don't know if that makes a difference. I have a friend who makes them (she does a number of crafts including pottery) - I had her make a few for me to give as a gift. Hers were a darker color but she said they lighten up over time. She does them as a way to preserve and recycle things that matter to people - like Grandma's broken china. My SIL's grandmother's china didn't survive shipment and she was heartbroken, so I had her send it to me, and I had my friend make outdoor stones for her and some indoor decor items for her 2 daughters (the sort of thing you'd put on a mantel). So I don't think the china would hold up to a lot of walking, but the cement would. There's probably a sealant you can put on for that purpose. If you want me to find out, let me know.
I'd try a kit, frankly, just to be sure you like the process and want to invest a lot of time in a whole bunch of them. You could make one to put in a garden where it doesn't get walked on, and then branch out after the first trial.
After that you can work with a good garden center or hardware store that sells the materials. Sometimes they give classes on technique and tips which would be worth your time. There are some areas of the country that seem to think spring might be coming one day, so classes might be starting up soon! (We're in New England so we know spring won't come until April 30th, but you might be more optimistic!)
What we did (my husband's idea, and a good one!) was to brace the mold on some paper, and then make the design on that paper with the stained glass shards and the little stencils for the letters. We played with the design a lot to get it just right. Do take the time to do this step! (If you use stencil letters, you only get 1 or sometimes 2 of each - so use a small piece of post-it or even something like a bunch of dimes as "place holders" for the duplicate letters.) Then once you mix the cement and pour it, you just pick up the pieces or letters from the paper template and place them in the wet cement. For kids especially, once the cement is hardening, this is not the time to start playing around with the design!