If you can find a gps that works indoors maybe, but most of them don't. As far as the radio, anything is possible if you have enough money. There are Wifi modules RF modems , 900mhz modems, 433 Mhz radios, 2.4 Ghz, and who knows what else. The distress call could be a GSM shield. I think there is a GSM +GPS shield. There are Ethernet shields for sending messages to the web. The pulse monitoring is probably the easiest part. There are 5.8 Ghz video transmitters You need to separate the modules and post each individually since no one sub-component belongs in the same category as the others. You need to define your budget first because the advise you get will be useless if you can't afford to follow it.
You might be able to use this: