I have a 2006 honda fit/jazz 1.3l i-dsi with a CVT trans and its my very first car. the car vibrates with some noise during low rpm specially in a stop while shifted in drive and gets intense with the AC on.

Another issue that i noticed is that as soon as i shift from park to drive after getting it warmed up from a cold start the rpm drops from normal 700+ to near zero with the AC on and stays to near zero with a lot of vibration and vibration noise (its quite scary) it only happens once after getting the car warmed up from a cold start but the the car does not stall it still runs (without stepping on the gas, just letting the car run by itself) but slow not its normal speed. But if I start her up and shift to drive after a short trip and slowly accelerate it just vibrates, no rpm drop.

Acceleration is quite good and i cant feel much hesitation,,,,, and as it reaches 1000+rpm, or if i shift it on park or neutral during a stop the vibration disappears.

Am I looking at an engine problem or a transmission problem??

What I tried:
I changed the spark plugs, and changed the transmission fluid, scanned with no DTC no check engine light. T_T

PS:
I have almost zero knowledge about cars, and I absolutely have no idea about its history, it was sold to my parents by a relative and was given to me with a condition that I drive my mom to work and pick up her up everyday with it and if I ask my relatives about the problems they experienced with the car, they would just answer me with some flowery words about how good the car is and how its well maintained (Its leaking at least two types of fluid btw!!! and when i asked them with the leak to which they answered me with "its a normal car thing")