Can I run pipe though walls and floors?

You can but you must ensure the pipe is protected: with a bulk head fitting (if used) or rubber grommet, or something equivalent.
It must also be 25mm clear of all electrical services (even extra low voltage) protected from stresses, vibration, and protected from kinking and chaffing (abrasion)(See Clause  5.2.1)
Protection is even more important with hoses!