My DHG had grown fine in my 10 gallon without CO2, just liquid ferts but I also had LED lighting so I'm not entirely sure.
Any moss would grow on wood, I really like both Taiwan and Christmas moss. But my real favorite is Flame Moss! And yes they can all be tied on with thread, I actually used purple thread for one of them and silver thread for the other haha but it's all the same really.
For red plants you can do red wendtii crypt, rotala, broad leaf ludwigia (Ludwigia repens), purple cabomda (Cabomba pulcherrima) is nice with high lighting, or red flame sword (Echinodorus sp.). Unfortunately to keep most red plants red, you need high lighting, same thing happens with any cabomda. If you keep it in a darker light it will be a very dark green but in high light it will turn bright green which is what it's supposed to be. Plants that will eventually be red, start off green and may stay that way in lower lighting.
I really want to have a nice little carpet in mine but I'm just still nervous about what the stock light can actually support. Its an LED but there aren't any specs on what strength. It would be easy enough for me to upgrade the lighting with a dome fixture and CFL bulb rigged up above the tank, I have extras of both laying around, but it won't look nearly as nice. I might just have to suck it up and accept I can't have it both ways right now, maybe eventually I can upgrade to a nicer LED for the tank. I'm considering trying some Marsilea hirsuta (dwarf four-leaf clover), worst case scenario would be that I end up moving it to another tank or it dies, neither of which would be new things for me :p. HC would be my top choice but I think the clover stands a better chance with my current lighting.
There are some great mosses available, so far I only have java moss thats yet to be attached to anything, so it just floats in clumps around the bottom of the tank which the ghost and cherry shrimp love at least lol. I think the mini Christmas moss is pretty adorable, but recently saw Anchor moss for sale on one of the sites I like for aquatic plants and it looks a lot like Christmas moss, but apparently grows much more quickly and densely which sounds awesome.
And yeah, red plants are tricky in low-moderate light tanks, or at least keeping them red definitely is. Certain ferts can help to a degree, but most really need the extra light. I really do want to find something that will add at least a little color to my tanks though too, so have been looking at the different options quite a bit. I have at least 2 of the plants already mentioned that actually did have a lot of red when purchased, but are now green, which I was prepared for but was still sad lol.
I re-did my 5g hex yesterday and can't decide if I like it any better than how it was before lol. I did attach quite a few pieces of java fern to the pieces of driftwood I used for the hardscaping (with just plain brown cotton thread though :p). Java fern at least is something that I have an abundance since it can literally survive anything--even if the leaves die the rhizomes remain viable and happily regenerate. All my java fern "windelov" are actually from the original ones I purchased in one of the small tubes at Petco as my very first aquatic plant starting out, so that was kinda neat. It definitely needs more background plants and I think at least one other type of moss besides java moss used creatively would help a lot, although that will have to wait until I have a little more disposable income to put towards more plants lol.