It is not possible to convert an analog television to a digital television. However, by using a digital set top receiver, it is possible to receive digital signals and deliver them as an analog...
Check the user's manual. Most TVs made in the last 2 years are digital. For sets older than that, you can find out by going to the manufacturer's web site.
For a TV with no video imput u could go and get a RF-modulator this plugs in to the back of your TV in a cable plug in and has video and audio plugs it also has a plug for a cable wire.
DVRs are compatible with most any cable, satellite or antenna setup. Your exact setup instructions will vary according to the type of DVR you purchase. You'll need to review your owner's manual for...