Leaky transmission fluid - 2001 Saab 9-3

On a parked level surface, warm up the motor to operating condition; while the engine is running, check the transmission fluid level by removing its dipstick.
Check your owner's manual if you're unsure how to check your vehicle's transmission fluid levels.
The color of the transmission fluid should be red and have no burnt odor to it. Should there be any discoloration or burnt odor, the transmission will need repairing by a trained ASE certified transmission specialist.
If it is only a matter of adding transmission fluid (see recommended fluid type in your owner's manual), keep the levels between the minimum and maximum levels- please do not overfill.
I would also check the area where the car is parked overnight for staining or puddles from a leaky transmission.
If the transmission is still experiencing shifting problems, there could be a problem with the vacuum modulator or something electrical with the sensors in the transmission or with the bands and clutches; again, a qualified mechanic will have to use computerized diagnostic tests to pinpoint the problem.

I could not find a specific video for you car, however the youtube video below is a generalized one that gives you the basic steps.
Auto Repair How Do Check or Add Automatic Transmission Fluid to My Car or... also walmart and other autopart stores sell transmission stop leak. https://www.walmart.com/ip/BARS-LEAKS-TRANSMISSION-STOP-LEAK-CONCENTRATE-11/192317005?wmlspartner=wlpa&selectedSellerId=837&adid=22222222227056015285&wmlspartner=wmtlabs&wl0=&wl1=g&wl2=c&wl3=159322577259&wl4=pla-268762134218&wl5=1015220&wl6=&wl7=&wl8=&wl9=pla&wl10=112343835&wl11=online&wl12=192317005&wl13=&veh=sem

Oil leaking around a starter is usually one of three possible things.
If it is motor oil, then suspect the rear main seal.
It it is auto trans fluid, it could be from the transmission front seal or the torque converter
If you have a manual transmission, it could be clutch fluid leaking from the slave cylinder, or a leaky front seal from the transmission.

no the tranny wont have to be dropped if it is just a leaky pan gasket.

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Fluid by the back wheels could be an indication of a brake fluid leak. Check the reservoir on the master cylinder for brake fluid level. If it's low, you've identified that you have a leaky brake line and should replace it immediately. If the fluid is full, it's possible that you've a transmission fluid leak that traveled along the undercarriage and is dripping by the back wheels.

For the fastest indication of what the fluid is, check all the fluids, power steering, auto transmission (if equipt) clutch if it's a manual transmission etc

TRANSMISSION LEAKS COME FROM TRANSMISSION OIL PAN GASKET LEAKING.OIL COOLERS LINES LEAKING.LEAKING AT TORQUE CONVERTER FRONT SEAL.TRANSMISSION SPEED SENSOR SEAL LEAKING.FRONT AXLE SEALS LEAKING AND LEAKING AT TRANSMISSION COOLING LINES TO RADIATOR.CHECK ALL YOU WILL FIND LEAK.IF YOU HAVE FAST LEAK OR PRESSURE LEAK.WITH CAR RUNNING IN PARK EMERGENCY BRAKE APPLIED LOOK UNDER CAR IF YOU SEE FLUID LEAKING OUT IN LARGE QUANITIES.COOLER LINES LEAKING OR TORQUE CONVERTER FRONT SEAL LEAKING.IF YOU HAVE SLOW LEAK THE LEAKS HAS TO BE AXLES SEALS OR PAN GASKET LEAKING OR VSS SENSOR SEAL LEAKING.

It is probably a hydraulic clutch. Check the fluid. From your description, I am understanding that the pedal feels normal but you are unable to put the car in gear when you push the pedal down. You probably have a leaky slave cylinder on the transmission, but it is possible to have a leaky master cylinder (on the firewall, aligned with the clutch pedal). Check your fluid, if it's empty fill it and bleed the system. You probably have a really big air bubble in your clutches hydraulic system. Usually you can get away with not replacing the leaking part for a bit, just keep an eye on your fluid, and save your pennies! Good luck!!!

If you have an automatic transmission, check the transmission fluid level. If the fluid level is low, the transmission will not engage.

If you have a manual transmission, check the clutch fluid level. Look for a leaky master cylinder or slave cylinder.

Transmission is seeled you will need to bring it to a dealership to have it checked, there is no way for you to access checking your fluid levels without doing this.

The cause could be transmission leaks from any number of sources but it should be investigated. Check the transmission fluid level after driving it awhile to warm it up. The fluid should be red, and within the guide marks on the dipstick. If it is dark, it is probably time for a flush. But you still need to address the basic problem which could be a leaky pan gasket, solenoid pack, dipstick filler tube, etc.

To find out which it is you will need to go under the vehicle with a flashlight and check for fluid "tracks" coming off the transmission.