Does Speaceblock work with Space Exploration 0.3?

Not yet. It will need a more fundamental change to have only Nauvis be a water world. This will take time to figure out how to code it.

Where did all the trees and gardens go?

Currently the space-exploration mod triggers the alien biomes "frozen" terrain tile and that breaks the seablock spawning of the gardens and trees. To avoid this, disable the "Frozen" terrain tile in the alien biomes startup mod settings.
If you're already too far along in your base to want to start over, here are some commands to spawn in enough to get you by:

/c game.player.insert{name="desert-garden", count=50}
/c game.player.insert{name="desert-tree", count=10}
/c game.player.insert{name="temperate-garden", count=50}
/c game.player.insert{name="temperate-tree", count=10}
/c game.player.insert{name="swamp-garden", count=50}
/c game.player.insert{name="swamp-tree", count=10}

Help I'm in a tech lock. Material science tech requires material science?

In the ScienceCostTweaker startup mod settings, turn off "Connect science packs".