Newbie question about green algae

OK....so I've spent the last 10 days fighting off the red slime....as a
newly set up tank just over 8 weeks old I was expecting this...it is a
15 gall nano reef....but to my dismay I discover green hair algae has
covered up my star corals....I've been blasting the stuff away with a
syringe but see not great recovery in what was my centre piece....

The coral itself is still attached to the rock...but no sign of any
polyps coming out....is it dead or do I need to be more
patient???....another piece of gold star polyps that went under almost
as soon as I put it in is now showing signs of life (not great but at
least some polyps are out and about)....

Is there anything else I can do other than keep the rock algae free? The
rock in question also houses a mantis shrimp and I want fish....should I
just sacrifice the whole thing? And get rid of the pest at the same time????

Very confusued newbie

Oh and these are the parameters pre water change...need to take them again:-

Sg 1.026
pH 8.4
Alk - higher end of normal on red sea kit
Calcium 450pm
NO3 High 12.5 Low 2.5
PO4 - 0.1

But I have now done a water change so need to test NO3 and PO4
again...the water matched all other existing parameters.....

I'm not really too keen on losing the corals...but if I have already
(it's been around a week) I need to know, especially with the colony
that has the mantis shrimp....

TIA
Gill

Gill