There are several types of designs for timber based fire doors, most will have lipping requirements but there are some without lipping. Where lipping is a requirement, density and thickness will be specified by the data sheet for the door leaf. As for trim allowances, fire door leaves can have different core construction types some having stiles and rails and some without. Some having a tubeboard core and some being completely solid. That's why there are variations in permitted trim allowances.
Select the fire door leaf most appropriate to its end use.
There is no 'one size fits all' when it comes to installation. The data sheet for that particular fire door leaf will provide the necessary details but you will also find BS 8214: 2016 invaluable for guidance. A new version of that Standard is due out this year I believe.