1) "A half-life is the time it trakes for half the mass of a given amount of a radioactive element to decay into its daughter elements"

Is it true that a sample decays "bit by bit"? Why only part of it decays (to daughter elements) and some other part is kept complete untouched (still being the parent isotope)? Won't all parts decay at the same time??

2) "If you were to begin with 10 g of U-238, after 9 billion years, or 2 half-lives, one fourth, or 2.5 g, of the original U-238 would remain.Three fourths would now be the daughter element Pb-206."

The decaying process of U-238 has many intermediate products (like Th-234, Pa-234,etc) before becoming Pb-206. Then is the bolded part true? (25% U-238, 75% Pb-206) How about the intermediate products, would they exist significantly, or would they just exist in an insignificant amount that it can be ignored?

3) "By comparing the amounts of U-238 and Pb-206 in rock samples, the age of the sample can be determined. Scientists know that from a million grams of U-238, 1/7600 g of Pb-206 per year will be produced by decay. The U : Pb ratio can be used only when the sample has not gained or lost lead or uranium since its formation."

Does anyone know where the "1/7600" comes from? I don't know how they can get the rate of decay per year, wouldn't the rate of decay be different each year, because of the concept of half-life (1/2 of the original amount for a certain time, right?)

4) "The half-life of C-14 is 5,730 years. To establish the age of a small amount of organic material, scientists first determine the proportion of C-14 to C-12 in the sample. They then compare that proportion with the proportion of C-14 to C-12 known to exist in a living organism."

Why should we determine the proportion of C-14 to C-12 in the sample? Can we just determine the proportion of C-14 (parent isotope) to N-14 (its daughter isotope) instead, like the U-238:Pb-206 in question 1?

Thank you in advance!