My parents did it with existing ductwork.
If both systems are forced air systems it's possible to use the existing duct work; however, with out viewing you project, I would suggest having an air duct specialist evaluate your system to determine if modifications are necessary .
Only if the existing duct was taking airflow from say, the kitchen, and blowing out of the building.
Diffrent color duct tape could work or sparkles.
Yes, a skilled professional would be able to install the proper duct work for central air conditioning in your existing home. Check in your area for a reputible business.
Air flow can be restricted by dirty duct work. Keeping the ducts clesn can increase airflow and make the system work more efficiently.
Yes cooling requires larger duct work. Typically you would size the duct work for the cooling system and heat will work fine as well
Sure, ductwork only carries hot air from the source to the living space. It does not matter what the source is.
If your apartment does not have duct work, the owner of the building has not had it installed. Perhaps they felt it would be too costly to install, or perhaps they are simply not interested in or see a need for duct work.
For round duct, measure from one side to the other, and you have the diameter.
Yes, the kind you use for duct work.
No not really because of its stickiness so no use string