Transmission and misfiring

My car was idling very roughly. A friend's mechanic drove 35 miles to my home and replaced all the spark plugs. It was still idling a little roughly, but seemed better. About two weeks later, the speedometer suddenly stopped working; it would only go from 0-20 mph regardless of how fast I was driving. During that same ride, I noticed the car seemed very sluggish and slow, especially on hills. As I got closer to home, an orange warning light on the dashboard came on. When I arrived home, the car had to strain to make it up the incline where I park. When I got out, I noticed a burning smell.

The manual says the orange warning light (an exclamation point) indicates the car is operating in "emergency transmission mode." The manual said to turn the motor off, engage the parking brake, and restart the engine a minute or two later and the light should go off. I did those steps but the light was still on. I started the car two days later, and the warning light still appeared. I drove to an AutoZone five blocks away for a free diagnostic scan that said two spark plugs were misfiring, the ignition coil needed to be replaced and there was some type of problem with the transmission.

A friend advised me to go to Aamco. I had a bad experience with Aamco decades ago but he said they are better now. Aamco has had my car since Tuesday afternoon; today is Saturday. On Thursday in the early afternoon they told me they were going to do an compression test, which cost around $200.00. I understand that engine test can diagnose a misfiring problem. When I called on Friday, they asked me to be patient because the test takes time and they had several other cars before me. From my research online shows that the test takes about a half-hour and should cost around $130.00 to $140.00.

My question is: Should I go get my car, pay for the compression test and take it elsewhere? Aamco closes early today. In four days, shouldn't they have been able to at least figure out what the problem is --much less fix it? I am a single woman and I worry they are just giving me the runaround.

Second question: Could it be that I just need to add transmission fluid? BMW says transmission fluid should last the life of the car, but perhaps there is a leak? I have an oil leak, so I might not have noticed if transmission fluid was leaking too. A friend advised me not to drain and replace the fluid, but to just add some if needed.

If I need to replace or rebuild the transmission, is it worth doing that on a 2003 BMW or should I get another car?

I'm sorry this is such a lengthy question. I greatly appreciate any advice you can offer. Thank you so much for your help!