You cannot date any fossil properly without knowing how much of the parent substance there was to begin with.
First of all, the actual fossil is not dated. It is the surrounding rock that is dated.
Secondly, it is the ratio of parent to daughter isotope that is used. For example, if you start with 1 g of uranium after 1 halflife you will have 0.5 g of uranium and 0.5 g of lead. If you start with 5 g of uranium then after one half life you will have 2.5 g of uranium and 2.5 g of lead. It is the RATIO that is important.
You can't know how much time has passed if you don't know how much sand was in the hourglass to begin with.
Last I checked an hourglass is a closed system so the amount of sand in the hourglass is how much you started with.
Scientists have found fossilized lobster shells from lobsters that are STILL ALIVE. Carbon dating claimed them to be over a thousand years old. But the lobster was still ALIVE.
Lobsters get their carbon from marine sources which are richer in old carbon. This is what causes the older date. Scientists know all about this effect. This in no way negates the accuracy of carbon dating for terrestrial samples that derived their carbon from atmospheric sources.
The second, that fossilization can occur rapidly.
You are confusing perminerlization with burial. The process of replacing organic material with minerals from the surrounding rock is a slow process. However, no one is claiming that animals and plants can not be buried quickly.