From my personal experience hydrogen peroxide 3% is fairly safe, what you want to do is spot treat the blue green algae (Cyanobacteria) don't just pour peroxide into your tank. There're a couple of videos on YouTube of a kid doing this if you need a visual.
Here's what I think you should do and I'm going by what I see in your pics.
First remove everything from your tank except water, fish, gravel, and media sponge. Clean/Remove as much of the cyano
as you can from the objects you took out of your tank. Maybe even pour some peroxide on them.
Next use a scrapper like a plastic card, scrape off and take out the cyanobacteria from the glass.
Then do a quick gravel vac to remove any loose cyano
from the gravel and water. When doing several water changes during a week try to keep them around 20%, doing several large water changes can cause unstable ph.
The purpose of all this to remove as much of the bacteria as you can to make treatment easier and to help prevent ammonia/nitrite spikes after the cyano
starts to die.
During peroxide treatment remember to keep pumps, filters, power heads turned off. If you choose to treat the cyanobacteria with meds you should know that it can kill your beneficial bacteria, I would use a syringe to spray some peroxide onto the bacteria that is visible in your tank. It doesn't take much just enough to treat the visible cyano
. After about 30mins or so you can put everything back together and turn everything on. Continue this method of treatment once/twice a week or as need.
Things you can do to prevent further outbreaks or help remove the current one.
If you have any blue actinic bulbs, I recommend you replace them with natural daylight bulbs.
Add a power head or air stones to improve water circulation.
If you have a hang on the back or canister filter thoroughly clean the the filter housing (not the media for your beneficial bacteria) and keep it clean.
From your pics it looks like all you have for filtration is a sponge power head which is fine but I suggest adding another or upgrading to a HOB
Hope this helps