I know I have a little nitrates at 5-10 and phosphate.02 to 0.
That PO4 level is actually the problem – not the NO3 level. Possibly a side-effect of the fishless cycle.
The base of your tank's bio-load – the microbial food web – is trying to grow in right now. But the high NO3 levels are causing a bloom/PO4-starvation cycle to happen.
The better course wold be to dose a little phosphate fertilizer into the tank to balance out what you've done so far with the carbon dosing.
THEN when things get to normal, I would
stop dosing anything for nutrients or nutrient control and focus on having a healthy, well-fed tank. Don't stock it up too fast, and don't let the fish get out of balance with the corals.
After the cycle is when I added the skimmer and carbon and started dosing vodka.
Skimmer is fine, but there's no call for carbon dosing at this stage of a tank's life.
I would stop carbon dosing now. (vodka, vinegar, nopox, et al.)
A new, healthy tank will have no problems getting rid of those nitrates by denitrification
and growing corals!
More importantly,
the nitrates aren't going to hurt anything in the mean time. There's no emergency. There's not yet a call to action.
Also I'm pretty sure it's diatoms no string no air bubbles just dust that easily is blown off.
That's not impossible, but Diatoms absolutely require a source of silicon in order to bloom and then keep blooming – they more or less permanently use up their source of silicon in the course of blooming.
That makes diatom blooms rare under normal, healthy circumstances. Usually just at the beginning of a tank.
Diatoms and cyano (among many other invisible things) both generally have a bloom while a tank is getting started....diatoms fade back once silicon levels drop....cyano fades out once there's a stream of nutrients into the tank. (They fix N from air, so they have "a role" at the beginning when the tank is completely N-defficient....or in otherwise N-defficient scenarios.)
Remember:
If you're fighting algae, you're doing it wrong. 