Also, like in the example of cross-border payments you can find banks involved, so in the example of block overly can there be some involvement of banks too ??
Lastly, how will be the exchange-rate decided and charge chose centered on what parameters ??
Bitcoin is universal. It is not a payment processor, as bitcoin is a unit of value in itself. I think this may be where you are confused(i may be wrong, but your question isn't very clear). No matter where you send bitcoin, it stays in the value of bitcoin. It does not change into a fiat currency and go through banks like traditional international transfers do.
This is one of the most attractive points of bitcoin, as there is virtually no difference between paying someone overseas and paying someone right next to you.