For your mystery algae, you should consider oomycetes as well. Some of your photos look like you have oogonia that perhaps belong to Pythium sp. Also consider that you have multiple species growing!
I'm sure there is a whole symbiotic culture of different things in there. It's likely one could by oomtcetes but to me the cell shape and size of the large organism seemed wrong. However the only fungi-like organisms I look at in a professional context have been dead for a few million years so I could be wrong.








