Non-Muslims can certainly produce and distribute halal food. A Muslim is only required to slaughter the animal or bird whilst blessing the animal in the name of God. Any halal food can be produced and sold by a non-Muslim.

Halal certification process starts by making an application to a chosen halal certification body. The process flow, fees and time frame vary from organisation to organisation; however, the process generally involves determination of scope, detailed scrutiny of your products and ingredients, audit of your manufacturing facility and processes employed therein, periodic surveillance activities (involving an Islamic scholar and/or Muslim auditor) and subsequent renewal where applicable.   

Food containing haram (or non halal) substances is not halal for Muslims to consume. This includes pork/pork derived substances, ingredients derived from animals not slaughtered as halal (e.g., animal rennet, animal based E-numbers), intoxicating substances (ethnol/ethyl alcohol). Halal food contaminated with non-halal food substances becomes non-halal for Muslims to consume.