Battle Cruisers

There is no Battle cruiser Hull size. The ships I use as Battle cruisers are generally based on the Battle ship hill but with an emphasis on speed over fire power. I have also built heavy cruisers by trading speed for fire power but basing them on the cruiser hull type. It’s a mater of role not hull size

To get the battle ship hull you need to have tl5 in light, light medium, Medium, Medium heavy to research heavy hulls which give you the battle cruiser

Yes, generally battlecruisers (those of the WWI era) had the armor and speed of a cruiser and the firepower of a battleship. If you want to duplicate this design I think you should invest heavily in the cruiser hull size technology (up to the maximum level) in order your ship gets enough tonnage to cramp heavy armament, while having enough engines to get a decent speed (battleship hulls are always slower than cruiser one’s).

Also Battlecruisers tended to be light on armour compared to similar firepower ships, they were strike weapons who's speed was meant to keep them safe, and firepower was meant to outrange and outkill everything smaller.

The Battle Cruiser is one of the Neostandard hulls:

Wiki Neostandard Article

SpaceEmpires.net | Space Empires Wiki

Battlecruiser in SE5 is, IMO, a cruiser hull large enough to mount a Heavy mount gun.

This definition pretty much fits the historical one -- a cruiser speed and cruiser armored vessel (maybe a tad more armor) with near battleship firepower. Any cruiser 800 kT (level 6) to 1000 kT (level 10) in SE5 pretty much fits this description. Heck, Battleships start at 850 kT (level 1), so as soon as you hit 850 kT with cruisers (level 7), you are definitely in "Battlecruiser" territory.