There seems to be a lot going on.
Surname change:
If you and ex-husband agree, this is a simple online process. If you don't agree, it goes to court.
As your daughter is 7, under Norwegian law she will need to give her preference in court. So the matter will be resolved. If you are the primary caregiver, the court is unlikely to approve the change.
Raising daughter as Muslim:
The father has no doubt converted to Islam to marry his new wife, and it follows that he will want to observe Muslim traditions during his time with his daughter.
Under Norwegian Law, as the main caregiver you can decide which school she goes to, but during his visitation time, he is legally able to take her to a mosque, teach her about Islam, share halal means with her, etc.
Formally converting daughter to Islam:
Under Norwegian law, he cannot formally allow her to recite the Shahada and become Muslim without your consent. When your daughter is 12, she can then give the court her opinion, and the court will approve or deny the request in her best interests. When she is 15, she can make her own judgment.
Summary:
Without your consent, surname change cannot proceed
Without your consent, your daughter cannot be formally become Muslim
With or without your consent, your ex-husband can raise his daughter as a Muslim during his time with her
So, tone down the hyperbole, focus on the law and process, get legal representation, and keep the best interests of your child in the forefront of your mind - and put your repulsion of Muslims and frustration at your divorce from your ex-husband on the back burner.