I can help in part .....
..... I have an alarm at my holiday home which does part of what you're looking for. It is battery or mains operated and when tripped (P.I.R or door sensor) sends a signal to my mobile telephone. I can either, turn it off and reset it or let it continue to sound and call for assistance if I'm not close by. It has the option of a siren or silent alarm - quite sophisticated really considering the price.
It cost me about £25.00 from a local electrical wholesaler however, I have since seen them advertised in those stupid magazines full of doormats, double slippers, bird feeders and things for catching spiders.
Unfortunately, it doesn't send off a GPS signal.... I can't recall the make or model but if I do, I'll post it here.
Buy it & Use it, then sell it and buy something bigger