1) Space ships that are directly brought over from canon are allowed to retain their unique quirks, and that applies to the Arcadia and its autonomy. In this case the Arcadia and its consciousness would be considered separate entity from its creator, and both can coexist in Space Race at the same time.
A personal space craft from Cowboy Bebop is <200 meters and would be a Small ship.
The Arcadia (right above the Lexx ship and to the right of the Titan A.E. ship) is ~1000 meters and would count as a Large ship.
A Buy-N-Large ship from Wall-E (~2000-4500 meters) would count as a Large to the Expense of Everything Else ship.
Something like a Star Wars Star Destroyer, a Halo Forerunner ship, or Warhammer 40K Dreadnaught (10000-20000 meters) is more suited to being an event setting by itself.
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2) Based on this no doubt highly researched image:
A personal space craft from Cowboy Bebop is <200 meters and would be a Small ship.
The Arcadia (right above the Lexx ship and to the right of the Titan A.E. ship) is ~1000 meters and would count as a Large ship.
A Buy-N-Large ship from Wall-E (~2000-4500 meters) would count as a Large to the Expense of Everything Else ship.
Something like a Star Wars Star Destroyer, a Halo Forerunner ship, or Warhammer 40K Dreadnaught (10000-20000 meters) is more suited to being an event setting by itself.