Do green algae form obligate symbioses with fungi? I understand that obligate symbioses means that the two organisms cannot live without each other and are in a symbiotic relationship, but do green algae from this with fungi?

Yes, Lichen are composite organisms of green algae (or cyanobacteria) living togther with fungi.

In most cases the fungi-part is completely dependent on that symbioses and is completely dependent on the symbiosis. For the algae it seems that some species can survive on their own, but not necessarily in the same enviroment as the lichen, while other species may again be completely depedent on the symbiosis (see also the comments).