+1 for Backblaze. They have a convenient backup software too that works great. I backup my parents laptop using it, and use their S3 storage for my NAS backups.

This would depend on whether the limit is defined as ingress or egress or both. For example AWS has free ingress traffic from the internet but there is a cost for egress traffic to the internet.

A better solution would be to find a unmetered service, which means that you have a fixed transfer speed (e.g. 500 Mbit) but have unlimited bandwidth. OVH offers this in their VPS products.