Can this not be: "they ring the police" ?
Report it. If we're talking about calling on the phone, ring is the same thing
They called the police???
Called = chamaram
When does "a polícia" mean the policeman, and when does it mean the police? What's the logic?
The police = A polícia
The policeman = O policial
Does 'chama' only mean 'call' in the sense of a phonecall or does 'calling over' (they are standing there, can you call -to/for/whatever- them?) apply as well?
Yes, "chamar" is applicable for both senses.