If we're talking North America under the National Electric Code (NEC), dishwashers must be on a dedicated circuit. There can't be a spare plug someone could plug, say, a vacuum cleaner into.
Really, it's best to run the yellow non-metallic cable right to the junction box in the dishwasher and nowhere else. This solves a bunch of problems all at once. No special armor is required, just run it.
Your area may, probably does, require an electrical permit for this work. For good reason too.
Most inspectors would require the hole be sealed tight, to prevent a garage fire from spreading to the kitchen. Intumescent caulk is typically used, but messy and sort of toxic. There are alternatives, such as a little doughnut of sheetrock. Your floor is wood, so it hardly makes sense to do much more than prevent air from entering the hole.
"Fireblocks can be constructed of materials such as 2 inch nominal lumber,
structural wood panels, gypsum board, cement fiber board for larger fireblock, and batts or blankets of mineral wool or glass fiber, loose fill insulation, and caulks, sealants, and putties for smaller fireblocks. Similar text appears in the IRC. " Jointofeu® fire ropes are an option.
You want to seal the hole for air anyway, to save on heating/energy/carbon costs.
See also Does a garbage disposal and/or dishwasher need to be on a GFCI?