yes you can reculture the algae species again. freezedring is just a preservation method and by providing appropriate nurient media and conditions you can revive the freezedried species. 

I think, that for the most algal species it would not be possible. It could work with some cyanos.

best way to find out is just try it.  Species are highly variable.

Maybe if you have resistant cells in the culture or cysts from a late phase of a batch culture. Or cells with a lot of mucilage that might protect them from the dryness enough to recover them after when you add into media.

Agreed with Grant Mitman, just test and watch if you recover a culture from freeze dried material, but also see if the culture remains reliable to seed after some new batch cultures. It might happen that the culture can degenerate as I’ve seen before with cryopreserved cultures.

I'm not sure its possible. Please reture to the method of freezdrying.

It will deactivate the cell functionality. I have tested for three different species (chlorella, scenedesmus, spirulina) and was not able to obtain any growth.