The distance Blutooth works depends on the transmitter (on the Dexcom) and the receiver (your phone).
The maximum distance Blutooth works is 33ft but if you have walls, etc. in between this could reduce the range.
However, there is no point having an alarm going off in another room when you are about to have a hypo. It would make most sense to have it with you at all times.
You say you have a pump. Depending on which pump you have, you could use the pump as the receiver for a CGM. For example, the Dexcom G4 uses the Animas Vibe as the receiver. As I always have the pump attached to me, it makes sense for me to buy the Dexcom G4 so I don't have the problem of forgetting to carry my phone and/or receiver.
I think there is a different CGM which works with the Medtronic pump.
As for extending the life of the sensor, all I do is restart it when it expires.
However, I find my body rejects the sensor (it doesn't like having foreign bodies stuck in to it) which limits the lifespan of the sensor. Typically, I can get mine to last about 10 days. My last one lasted 17 days and I have read about some people getting theirs to last more than 3 weeks.
@tim2000s mentioned attaching it to your arm. Unlike the Libre, the recommended place for the Dexcom is the belly. Many people use the arm and have no problem. As it is much bulkier than the Libre, I find the arm too obtrusive. But then, I am vain.
The explanations on the Dexcom website are very simple: it is worthwhile having another read armed with the information you have got so far from this thread. Might make more sense now.