Diode are there to avoid conflict between your voltage source... with this, the higher voltage will win the race
Capacitor, 10 uF and more should be enough. For filtering purpose.
You could use 1N4xxx diode, bear in mind their voltage drop is around .6V so your 3V will be 2.4 volt when your battery is at full-charge.
The pic will work as long you haven reach the Brown-Out threshold voltage OR his voltage threshold depending on the osc speed you're using.
You could still use another much fancy system, this one work pretty well in many cases.
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