I would say the most likely answer on number one is not agate, it is more likely a macro-crystaline quartz and it does not look like chalcedony or chert. Something as hard as agate would not show fractures, if it was, they would look like conchoid fractures if this were agate. Conchoid fractures look like the fractures made on arrow points made by neolithic man in flint arrowheads. The matrix material could be anything. There is no scientific answer to why a silicate forms into quartz or agate. Quartz is a macrocrystal formation and agate is micro crystal. Both are formed by silicates exactly the same until subjected to geological conditions where the final outcome is one or the other.