If I have mirror routing on my 0345 number, and I add DNI to my 0845 number, what number will be displayed if the caller dials my 0345 number?

If you have DNI added to your 0845 number it will display the number the caller has dialled regardless of whether you have mirror routing on your 0345 number. 

Therefore if the caller dials your 0345 number it will display the 0345 number, and if the caller dials your 0845 number it will display the 0845 number.