I don't use cell phones on cruises so I can't tell you much about that aspect. The information provided by RCI states it depends on your cell carrier and international roaming rates apply. All billing is done by your carrier.
As to the internet, on RCI the base fee is 55 cents per minute, but you can buy a block of minutes that lowers the per-minute cost. You can buy 60 minutes for $28, 90 minutes for $38, or 150 minutes for $55. Those were the prices last week.
Note that shipboard internet is not especially fast, and it can be off-line depending on the ship's location. On our Alaska cruise I think it was off-line more than it was working, and I never could get the wi-fi option to work so I had to rely on the ship's computers. Not sure if it was an issue with my having a Mac laptop or what, but those with Windows laptops seemed to be having problems too. I've never had a wi-fi problem on other RCI ships. I hadn't planned on lugging a laptop across the continent for no apparent reason, but that is what I ended up doing.
RCI doesn't have dedicated internet staff on their ships, so any problems you have are handled by the purser's desk. In other words you are really on your own unless a computer geek happens to be on duty at the desk.