You will have to shoot it to find out.
No
no, the 7mm is .284 bore, the .338 is, of course, .338
200-500 USD depending on condition.
$300-550, depending on exact model and condition.
No specific records. The 7mm Magnum is not a military round, nor is it specifically used in long range competition.
The start of long action cartridges is the 30-06. The 7mm Mag is longer than 30-06, so would it be considered long action.