Nope need centre fire.
Not necessarily true, it depends on the firearms dept that he deals with. Some will pass .17HMR for fox outright, some for "opportunistic fox" only, some consider it included when specifying "Vermin" on the FAC (in which case it could be an implicit approval for .22LR), others will treat it separately and put "Fox AND Vermin"
If you're considering HMR for fox, I'd speak to your FEO first and get his thoughts (as they do vary from area to area). I think most people on here however would suggest a small centrefire for a dedicated foxing rifle, regardless of what