Welcome to Android Central! Updating preinstalled/core apps may depend on the manufacturer. Some manufacturers (like Lenovo) make at least some of their core apps available in the Play Store, which makes it easy to update them. Others only update them as part of a system update. When I searched for LG in the Play Store, I didn't see any of the main preinstalled apps, so they probably have to be updated through a system update. (BTW, @
PJRed2008, the OP has an LG, not a Samsung device.

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Unread count badges can sometimes get stuck. Try going to
Settings>Apps, tap Menu>Show System, then look for something called BadgeProvider (or similar). Select it, then Clear Cache/Clear Data. Now see if the badges work again.
Can you give some more detail about the messaging app's problem with certain MMS messages? Does it say "Tap to Download"?