Cant see the vid in work, but what you describe is very common, they all tend to do it, some days worse than others.Hold the key on the starter for longer until you are sure that ut has fired up properly
Video is private mate
Coil packs, PCV failure? worn out cam follower fuel pump?.
I don't like the sound of those Apr hpfp as they are prone to failure as I've been reading about them and users having to fork out for new ones
Mine struggled with similar issues. Bought a new battery and it worked even though battery test showed my existing battery seemed fine.Also as good practice I now turn the key over halfway until the lights come on. Wait about 3 seconds until the lights go off and then I turn the key fully and even in the cold the car now starts perfect.It used to judder a bit before I did this.