Anyone can listen in on cell phone conversations. A receiver is required to pick up the signal. There is additional equipment to help zero in a specific number.
Anything that sends out an electronic signal into the air waves must be vulnerable to tapping. If they can do so on TV, they probably can do so to you.
Cell phones broadcast radio waves through the air. Anyone with the right kind of receiver can hear conversations. Anyone with sophisticated equipment can specifically monitor a given cell phone number.
Yes. Although the older analog phones were easier to tap, with the proper equipment, digital phones may be as well. The equipment is expensive, but available.