The ARR of the timer determines the period, Update is when CNT==0, the cycle after ARR==CNT
If you want the TIM to generate 8 pulses,use an Advanced TIM (TIM1/TIM8 on most parts), set the Repetition Count.
You don't want to access the TIM or GPIO 8-bit wide
To drive periodic signals onto GPIO use DMA to write the 32-bit wide GPIO->BSRR, use a DMA than is trigger from a TIM UPDATE or CCx signal of choice. Set the period to control how the APB/TIMCLK is divided down to the signal placement interval. The trigger doesn't need to be a pin, you can just set the TIM up as a timebase and use the TIMx_UP connected DMA channel/stream.
The BSRR allows you to control single or multiple pins on a bank going high or low.
You will need to make a "pattern buffer" describing the sequencing of the pins, you'd need to make 8 entries to turn the 0xAA to PA0 pattern sideways, high bits at position 0, low bits at position 16, ie 0x00000001 PA0=High, 0x00010000 PA0=Low
