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The anubius doesn't have to be on the wood, but it definitely does better with the rhizome above the substrate. It will eventually send roots from the rhizome and achor itself, sometimes it is just difficult to keep it in place until it send out roots. Maybe tie it to a small stone to keep it in place if it wants to move. My experience is that having the rhizome buried doesn't kill it outright, but I thought I would mention it because it apparently is a possibility. Having said that, I have a Anubias barteri
with the rhizome exposed next to a Anubias hastifolia
with the rhizome buried and the barteri is growing great while the hastifolia is not. It hasn't died, but no new growth at all. I plan to pull it out of the substrate at some point and see if it improves.
Yes about the algae, there will always be some and it is not feasible to eliminate it 100%, but T5 HO is a lot of light. Your tank looks fairly tall so it can use a bit more light than a shorter tank, but having that much will require more attention. Dial back another hour or even two on the photoperiod if it looks like its gettting out of control.