My battery in my 86' W126 300SE marked "16.8.95".
(1) will the old battery make the car hard to cold start??
(2) If yes, any precaution, suggestion, need-to-know, for the DIY battery replacement?? Please help.
(3) any "Memory Lost" on my car in battery replacement??
Thanks!!

Low battery voltage causes lower ignition voltages and slower starter speed. If the voltage drops below 9v various control units reset or drop-out. Obviously if its too dead nothing happens.

The biggest precaution is more of a warning as its a lot of trouble to avoid. If you have the original Becker radio it has a unique theft system. Normally the only way to set it off is to remove the radio while the cars alarm system is set. Unfortunately the programming that controls all that is maintained by a small battery internal to the radio. If that battery is dead the radio will go to ---- with the disconnection of the car's battery. There are means to go around this but the eventual repair is to replace the battery in the radio and have the dealer recode it for you.

The point here is that if everything is working you DO NOT need to take precautions to save memories on that year model.