That is not your transmission, but it more than likely caused by extreme turns over 5mph. That popping sound is unique to Husqvarna, as when you make sudden quick moves, you create high hydraulic pressures and it is the machine protecting itself from harm. You have a great mower, so I would take it to the dealer and let them look at what hydraulic system is actually doing. If it goes away if you slow down, then you're good to go.

Your best taking it to a good lawnmower repair shop as they will have the tools to find and fix the problem.
I'm assuming you mean there is no power going to the left wheel? I am not very familiar with Husqvarna mowers but this sounds like there is a problem with the drive system or transmission links.
You could try safely raising both back wheels, (drive wheels), off the ground onto axle stands. With the power OFF turn each wheel by hand. They should turn smoothly and feel the same. If one side is slack, tight or 'notchy', that is the side where your problem is likely to be.
Carefully start the mower and GENTLY apply power to see if both wheels turn together.
The popping and jerking could be the drive system slipping and missing.