There are nearly 7,000 ISPs in the United States alone. While some of them do supply 24 hour customer service, the smaller companies are likely to only staff call centers during business hours.
This depends on the area of the Country that you live in. Many of the larger ISP's do provide PC to phone services, but it is not available in all areas.
I was not able to find any information linking Internet Service Providers to webhosting and an offer of unlimited bandwidth. I would think that most, if not all, ISP's are going to limit bandwidth...
"Yes, the CSA Travel Protection does offer 24 hour service for its customers. During emergencies such as hurricanes and other natural disasters, they usually have free service."