Cool idea, that elatine triandra looks nice. My Rotala is growing really low and bushy in the front, and this looks similar but even lower. I read a little about it, and it looks like it's a stem, but will also spread? Do you just let it spread, or do you replant the trimming like a stem plant?
BTW, nice tank! looks like a similar basic driftwood structure as mine. One problem I am having is that BBA seems to love the upper bare branches that are exposed to lots of light . . . I am still working on the CO2 levels, which might help.
It will grow like most carpet plants, spread out along the substrate via runners.
Spot dose the bba with excel (i find it works better than h202)with the filters off, let it sit for 20 min. It should turn the bba a red/grey color within 6 hours or so, which is then easier to remove.
I seem to always get a few patches of b.b.a on wood in a new tank, as your plants are growing, the tank has a higher c02 demand than say a month ago, so this causes a drop in c02 levels and can induce algae, especially b.b.a as it likes fluctuating c02 levels. So stay on top of the c02, increase it slowly as your tank fills in more densely. make sure you have plenty of surface ripple, and attack the algae as you see it before it spreads.
edit, another idea on the bba. The way your outflow is setup, the flow is broken up between the heater and the c02 reactor. C02 becomes harder to dissolve as the ppm rises, so when the tank has say 30ppm, c02 is going to be harder to dissolve than say at 10ppm. This will create a larger pocket of air in the reactor later in the c02 schedule, which will also create more back pressure and push more water toward the heater, so this is probably creating a large variation is the amount of water being driven through the reactor, in turn creating a fluctuation in c02, which bba loves.