Torque converter issue?

My car is a BMW 5 series with the ZF8 automatic transmission. It doesn’t shift perfectly – jerks a bit in all gears shifted in the first drive of the day, for around 10 miles then it becomes much smoother. 1-2 gearshifts are sometimes noticeable, especially if the acceleration is very slow – or every time at any acceleration in the first 10 miles.

Also, there is a jerk similar to a jerk happening during a gearshift (like a hard engagement of a clutch) which happens in 1st gear without shifting in 2nd! It happens for example if I accelerate slightly from a dead stop in manual mode gear 1 and can be felt around 1200 rpm. Is this the torque converter clutch, engaging in gear 1 at 1200rpm? (car is diesel).

Also, when braking and almost coming to a stop there are two moments when a jerk can be felt (like a bump that is affecting my linear braking). Maybe it is shifting gears 2-1 and 1 disengaging?. When the car has just stopped very rarely a small jerk appears – car is trying to lurch forward for half a second.

Can all these jerks (1-2 gearshift is always most pronounced compared to the others) be caused by a failing torque converter?

There are no errors and the transmission has been serviced. There are no other symptoms.