Impossible to answer without a detailed description of all markings and features.
$200-$300 if 90% or better.
The Browning. No Contest there.
You will have to call Browning.
BAR stands for Browning Automatic Rifle, not browning association rifle.
The M-1918A2 Browning Automatic Rifle (BAR) was not built until 1918. $270 USD in 1941 $23,000 USD regestered full auto in 2012 $4300 USD A-3 semi auto $320 USD open market price (used)
Browning automatic rifle
The BAR
.30-06
Browning Automatic Rifle
Yes
Possible, but, not likely
probably browning and remington they are used the most