School Safeguarding Lead here. Taking the emotion out of it and focusing on the facts, these are the pertinent points if I've understood correctly: Your DD was in a relationship with this boy and she ended it. Over the past 7 weeks he has turned up at your house uninvited on numerous occasions. On each occasion he has been told she does not want to see or speak to him, but this has not deterred him. He has sent your DD numerous messages professing his love and asking her to take him back. She has tried to block him on social media, sending a clear message that this contact is unwanted, but he continues to message her by creating new accounts. She has tried ignoring the messages, and when this didn't work she replied asking him to stop contacting her but this has not deterred him. He continues to turn up at your home uninvited, and has left unwanted gifts for DD on the doorstep. You have warned him that further approaches could lead to police involvement, but this has not deterred him and he continues to try to contact her. The last time he turned up at your home your DD became distressed and experienced a panic attack.
If you were a parent at my school I would strongly advise you to contact the Police and report this boy for harassment. If you didn't, frankly I'd be concerned. Although at 16 she may have the capacity to make choices for herself, your DD is still a child and sometimes the adults have to step in and take charge.
I would advise you against contacting his parents directly. IME this rarely ends well. However "lovely" they are, they are incapable of being objective and at 16 they have limited influence over his choices anyway.
As DSL I would also speak to your DD myself to ensure she understood why this boys behaviour is unacceptable, and to identify a member of staff she felt comfortable talking to in school so she could report any concerns or worries. It's likely his friends will come up to her asking why she has reported him, so I would emphasise that if this happens she needs to let me or another trusted adult know immediately and they will be told to mind their own business and leave her alone. If they don't, there would be consequences.
If she has classes with the boy we would look at moving him, or if this was not possible rearranging seating plans so she doesn't have to sit anywhere near him. I would find out where both their friendship groups tend to hang out at lunch and break and ask the members of staff on duty in those areas to keep an eye out for anything untoward.
I would speak to the boys Head of Year and we would be keeping a very close eye on him and his interactions with other students. He may also need some targeted support and a keyworker to go to, depending on his individual circumstances. We would also look at some whole year group tutor time activities or assemblies around boundaries, consent and healthy relationships, but that should be happening anyway.
IME the Police will most likely not be interested in criminalising a 16 year old for this kind of thing in the first instance. But they will explain to him in no uncertain terms that his behaviour is unacceptable and needs to stop, and what will happen if it doesn't.