Answer to "How do you find out the gear ratio?"There is usually a component info sheet under the cover in-front of the fuse panel axle ratio is in the lower right in the gray aria.
Answer to "Major loss of a/c oil but can not be found."First do not use dealers for HVAC unless your rich and like paying to fix the same thing multiple times. Second go to your local auto supply and get a UV light kit $20 -$30 the die fluoresces. In general A/C dye is green Third start pulling panels anywhere a HVAC component or line runs you'll find the leek . (I'd guess it's a evaporator) I do question the shops that have been working on your A/C you don't pressurize for testing you pull a vacuum . If the system is charged high side pressure can fluctuate from 110psi to 225psi and low side from 10psi to 60psi depending on system and environmental influences.