ARE all LCD TV'S didital ?

Answer 1

No.

Usually when people talk about digital TVs they mean that the TV has a tuner that can receive digital TV signals. Plenty of LCD TVs were made with only analog tuners before the government started requiring digital tuners.

LCD TVs that only have analog tuners will need a converter box to receive digital over the air broadcasts, just like old CRT TVs.

Perhaps this is confusing because the display electronics in all LCD TVs are digital. In addition, analog tuners of resent vintage are largely digital in their design. These are completely different issues which only concern people who make & repair TVs.

For better or for worse, commonly used languages require a lot of assumptions about things; one of these is that when you ask about whether a TV is digital, you are talking about whether the TV can tune in digtial TV signals and not the electical engineering details of the TV.