You can call Remington at 1-800-243-9700 and go thru the menu selection. One of the menu options is to request information on your Remington based off the serial number. You read off your serial number and the guy looks up in the database the year the gun was made and what the original barrel was for that gun (if gun had barrel options like shotguns do).
Can't be answered without a serial number.
1000$
Check the date code stamped on the barrel. Look for the manufactured date link on the Remington Society of America for details.
$350.00
100-400 USD
I will first say that the Remington model 788 was made in 6mm from 1969-1979,at this time they are going for anywhere from 250-450 dollars depending on condition.
$500-$600
100-400 USD
Consider yourself lucky if you get 300 dollars for it.
100-400 USD
The Remington 788 model rifle was a great shooter in the few years that it was sold. A nice functional 788 in 22-250 should bring between $200 - $450 depending upon condition and any accessories (extra magazines, scope, mounts, etc. )
Check this table for the answer: http://www.remingtonsociety.com/rsa/questions/barrelcodes