"Connection reset by peer" means exactly what the second log file line says: Your Redis server didn't close the TCP connection, the client closed it. The answer to your question on how to minimize the disconnections depends on what's causing them. Why would a client that connected to your Redis server decide to disconnect?
The first step toward understanding why the client disconnected is: What kind of client is this?
- Is it a monitoring system that connects to test that your Redis server is available?
- Is it another Redis server process that's replicating data with this Redis server (in a primary/replica [used to be called master/slave] relationship)?
- Is it a client that connects to your Redis server to read or write data?
The expected behavior for each of the above type of client is often different, and the action you'll need to take to prevent the 'reset by peer" messages will be different for each of them.
Your other questions can't be answered without knowing what type of clients are generating these messages. In the case of other Redis servers, your monitoring system will tell you which ones are exiting/crashing (and therefore dropping their connections), and you can match those timestamps and IP addresses to the messages in your log. In the case of your monitoring system, testing and changing the code that connects/disconnects may be required. (it's common for monitoring systems to just disconnect instead of sending a QUIT command and waiting for the server to acknowledge)