The area in which things are baked and packaged does also handle nuts and the products are labelled as such. I do try everything within my power to avoid cross contamination and I label my products 'May contain traces of nuts'.
Vegan/egg free/dairy free
All products labelled as vegan/egg free/dairy free are made in a egg-free and dairy-free environment (though my kitchen does handle eggs and dairy)
I use separate utensils and equipment when baking.
As above, all products are labelled but as my kitchen also handles wheat and gluten ingredients please be aware that I use store-bought products that come with the label 'may contain traces of/or handled in a factory that produces wheat and gluten products'
I use a mix of tapioca flour, rice flour and potato starch as an amazing gluten free flour blend, this gives light fluffy cakes, chewy cookies and fudgey brownies.