The guide with all comments worked well for me. Thank you to everyone for their input.
I can confirm the additional steps mentioned in the comments:
* Part under vibrator last visible in step 60/61
* Three Mounting clips e.g. visible in step 51
* Two rubber / mesh parts left and right to lighting connector
* One rubber part under that chip visible in step 61
To attach the battery in place I used iPhone 5s/5c/SE (1st Gen) Battery Adhesive Strips mentioned in iPhone 5s 电池更换. I cut a small piece off it to fix the lightning assembly in place.
The iFixIt Phillips 000 screw river did not work for me. It seems to be just a tick to large and I damaged two screws with it. I used small Phillips screw driver labelled 1.5 x 45 that I bought locally.
The replacement fan's ribbon cable is a few mm longer than the original. I t will loop upwards a bit after mounting. The rubber lip on top of the old fan needs to be transferred to the new fan.