Yes, you need the proper equipment but it's no problem. Verizon, ATT and Tmobile all have devices that plug into your laptop to get internet. You can get satelite TV anywhere. The problem is tracking while your moving. If you just want TV at anchor use this Marine Satellite TV Tracking If you want TV while you are underway you'll need a far more expensive system but it can be done. Then you need to sign-up with a satelite TV provider.
Yes, as long as you don't get TOO far offshore. You can drill down to TV availability here: North American Coverage . Internet coverage is generally a bit better although it can be expensive. You may find you need two antennas to get TV and Internet.
Most people use a combination of WiFi and cellular services for near-shore Internet. Satellite TV is not unusual on board, and there are relatively inexpensive solutions for TV at anchor and docked.
Last I read up on satellite Internet service, to use it like you might at home would cost thousands per month in data charges. 3G or 4G cellular Internet access is very good, unless you have to download huge files or HD video files. I'm using 3G on my iPad, sitting in my salon right now. For this stuff, I can't tell the difference from being on my home computer. I've also received a good 3G signal several miles offshore, but it does depend on coverage and how close the antenna is to shore.
If all it takes to make her happy on the boat is TV and a cellular connection you are indeed fortunate. I have a TV antenna on the boat purchased from West Marine that picks up all the local broadcast stations as long as you are in the line of sight of their antenna systems. Keep in mind that when TV changed to all digital format, it meant that your antenna had to be able to see the station's antenna in order to work. Same is true for cellular telephones, but with the telephone you have lots more antenna towers to work with,