From my all be it limited experience if you dont wipe the leafs quite regularly you will get algae on them pretty much whatever the light is, a simple test is to wipe the leaf gently and see how slimy/sticky/grimy it is then give it a proper clean, it should almost feel rough to the touch...
My hc was hit hard with green thread in my last scape keep up the water changes and manually remove as much as you can and it will soon dissappear :) a tooth brush is amazingly good at removing the algae just spin it on to the toothbrush like spaghetti on a fork :)
Yes I hate the white it gets clogged to fast and can cause issues
Once youve done the filters you can see the increase of flow youve gained just lift the spray bar out of the water and see how much feature the jets go :)
Yes definitely remove some of that, it sounds ram packed, in a planted tank especially a heavily planted tank loads of media is npt necessary most people on here have somewhere between very little and half full :)
With your filters dont be to tempted to fill them up ive got an eheim 2217 and use a small layer of noodles like pic 3 and only 1 sponge using to much media and sponge will reduce the flow rate massively
I would definitely recommend an external filter the 501 is imo underpowered rated at 200lph id look for something like an eheim 2213 or similar
The eheim 2213 can be picked up on Amazon for around £30 and is a real bargain you wouldnt regret
I would 100% say your problems are flow and...
Id definitely look at the lighting and co2, I have the same size tank and similar set up I only run 7 hours lighy and use pressurised co2, yeast co2 can work but doe fluctuate alot which wont help with any algae,
Also one thing that stands out is you haven't mentioned what filter your using...