my problem is solved, so I just post this message to avoid helping people to take some more time for me. Although i don't consider this topic closed as i just have a part (the tinest one) of the answer and i am pushing to get it at full.
This problem has been solved for me by my hosting service guy. I don't have more details than that for the moment, but he did nothing about my opencart, just server stuff.
this issue was larger than the title as auto update was an issue on:
- cart list below cart button.
- cart page, therefore the topic title, because no auto updates although manual was doing it,
- checkout page, as if one payment failed, it did not allow me to change of payment option.