First time I saw this Longines with very special dial...need some advice from professors about the type and reasonable price for this. (It's 14k solid gold case)

 

Welcome! That's a refinished dial which will hurt the value. It's a manual wind that has (in order of probability) a caliber 23Z, 370, or 1x.68 inside. All are good movements. It's a front loading case, meaning the dial & movement come out the top after removing the bezel and crystal, which Longines started using around 1958 so it's probably a 60's watch. I'd say $500 or maybe a little more because of the value of the gold and the logo band. It will need a cleaning & oiling before you wear it.