You having it backwards, disks expand to ellipticals as they use up their gas.

Forming a disk requires collisions, and stars are too far apart. The gas in young galaxies does collide, which bleeds off angular momentum, allowing the gas to form a disc, then stars form in the gas.

Those blue stars you see in spiral galaxy arms will not survive a single trip around the core. They light up the region of compressed gas from density waves.

It needs to be faster, more like 3.4 km/s

Throwing an object at the escape velocity just means the gravity of the moon will slow the object down until that object is not moving relative to the moon. The moon orbits the earth at 1.02 km/s, so the object would end up orbiting the earth.

Throw something (2.38 + 1.02) km/s in the opposite direction of the moons orbit and it will end up with an orbital speed of 0, causing it to fall down to earth.