Hair algae/general next best step question

Hi all -

apologies for asking a question that's probably been asked a bunch of times but i'm at a loss for what my next best step is.

I have a 10 gallon tank, been set up for about 7 weeks, and stocked for about 3 weeks with 3 scarlett badis and two otos. I have the stock topfin 10 gallon filter with extra sponge stuffed in there (sponge has only been in for about a week). I do 1mL Excel every day or two, and starting last week I'm going to do the standard Fluorish once a week. For lights I have a 14W full spectrum LED (albeit a cheap one). No CO2, as of now.

I have quite a bit of brown hair algae, mainly on driftwood ,but definitely also on plants, and my main question is how do I best proceed, as I've heard and read different things.

- Lights - right now they're on about 8-9 hours a day. I will cut this back to 7ish probably, but for now i'm going to cut it to 4 for a few days before trying to rid the tank of as much algae as I can manually by scrubbing followed by a big water change. Is 7 a good duration for the future? Should I do this 4 day semi-blackout?

- Fertilizers - I've read that too much fertilizer causes algae, and I've read that too little can cause algae. Am I doing too much/too little/an appropriate amount?

- CO2 - I've read that it is the cause of algae (not enough of it), but I've also read it's not as big a factor. Should I start injecting CO2? Not looking to spend a huge ton so I'd go with one of those Fluval 45g kits, anyone know if they're any good? Mixed reviews online.

- As for the plants I currently have in there, most are doing pretty ok, though some of the red leaf plants are getting black in their stems and some leaves are dying off (sorry I don't know all their names, see pictures below). Are these ones lost causes? Should I do a big trim and get rid of any blackened plants?

- The scarlett badis I have are really picky eaters, which I read exactly 10 minutes after I arrived home with them, still mad at myself for not doing enough research. Right now i'm squiring in some frozen brine shrimp every day or two. Not a ton, I scrape some off the top of the frozen thing with scissors into a glass and use a syringe to squirt them in. The problem is, I don't see them eating it very often. They've been alive with me for 2.5 weeks now. Would they already be dead if they weren't eating? Because if they're not eating I assume this shrimp is contributing to my problem.

- If I take the wood out and give it a really deep clean, a) is that worth it and b) will that kill off a substantial amount of the good bacteria to the point it would be detrimental?

- amano shrimp, planning to add like 3-5, will they make a dent in this or will they just kind of help but not fix it?

thanks very much for going through all this to help me out!