“LFT blood test?”

Yes

Yes, it is definitely possible. One can have normal-looking liver function tests despite having a significant underlying disease in the very early stages of liver disease and the late stages of liver disease.

Yes, of course. By "LFTs" most people are referring to the ALT, AST, bilirubin and alkaline phosphate. Each of these may increase for different reasons, or multiple tests become elevated in different patterns depending on the underlying disorder. The AST and ALT tend to go up when there is any inflammation in the liver (alcohol damage, viral infections, drug reactions, etc.) but they can also remain normal and the liver can be diseased and even become cirrhotic while the ALT and AST remain normal.

Yes… it is disease dependent.