Can i solder a pic ic after programming it without damaging its data or functionality

YES, IF YOU CAN SOLDER EACH PIN WITHIN LESS THAN 2 SECONDS......A PERFECT SMOOTH SHINING SOLDER JOINT.

Yes, like the other answerer said, if you reduce the heat to just above melt, use flux, the right size tip, and keep the melt time under 2 seconds, there should be no damage. Don't reheat the joint if you make a mistake: flux and wick the joint clean (within 2 seconds) and try again. That should prevent a cold solder joint.

It depends on a number of factors; the type of tech the chip is made from (TTL or CMOS, other), your ability to control static, your soldering skill too.
I would recommend you solder in a socket for the chip to pug into.