"I am aware that you can watch tv on your computer but wonder if you can get digital tv this way too?"
Yes, you can get freeview, and standard "free-to-air" recievers fo PCs. I don't beleive anyone offers Sky Digibox receivers for PCs - but you would, of course need a card, anyway.
There are very few TV programmes available on broadband - nothing that would replace Sky, or freeview, at the very least.
"Also, our daughter works in China and I believe that, once on broadband, we can use a skype (?) phone to talk to her freely over the internet?"
If she has broadband too - then you can talk PC to PC and have a camera too, using MSN Messenegr, which is supplied with Windows - no extra software required. Thee are many other similar programs also.
You don't need Skype to talk to each other (see above) - but if you want to call her on her telephone, you would need a service hat provides this - Skype is just one - there are many others. Sipphone and Gizmo, IMHO is better than Skype for this. You will have to pay for this type of service - you may find other was of making cheap calls to China that work just as well and as cheaply. Gizmo calls are 4.9cents/min to China. Sipphone offers free phone minutes every day to China, including to mobiles!
I recommend you to get a USB headset (phones with mic) for making calls from the PC - and a webcam, for video calls - you'll never look back!