True
All somatic cells have same genes but the genes whose product is not needed are turned off. Some genes are expressed constitutively and some genes are turned off and on depending upon the requirement of proteins.
For question 3, it would not leak through the whole sandwich because the cell membrane is thick
The reason as to why fungi fossils seem so rare is that they are usually microscopic and often difficult or impossible to identify.
Not much information on fungi fossils has been documented. This could be because fungi fruiting bodies consist of soft, fleshy and easily degradable tissues which due to their poor integrity do not keep or preserve as well as animal tissue.
Even when available, it takes a trained eye to recognize fungal fossils. Not many people have the training and expertise to recognize the fossils.