As for your question a), the default TO is 10000 ms. This is defined as DEFAULT_MESSAGE_TIMEOUT in twDefaultSettings.h.
Regarding b), "sendCtlFrame: Error writing to socket. Error: 32" indicates that it failed with "Broken Pipe" Error and other following outputs are showing that attempts to reconnect with Thingworx Platform failed.
It might be helpful to review CommunicationLog.log on your Thingworx Platform to find how reconnection was happening during the time period.
I saw the log.
[DEBUG] 2017-03-20 15:48:53,951: sendCtlFrame: >>>>> Sending Ping. Msg: 14:48:53
[WARN ] 2017-03-20 15:48:54,46: sendCtlFrame: Error writing to socket. Error: 32
[WARN ] 2017-03-20 15:48:54,47: api:sendMessageBlocking: Receive failed.
[WARN ] 2017-03-20 15:48:54,47: api:sendMessageBlocking: Message 4 timed out
[ERROR] 2017-03-20 15:48:59,47: connect to platform: Server connection failed after 3 attempts. Error Code: 1114
Ping request has got timeout within 1 sec, so I suspect that "DEFAULT_SOCKET_READ_TIMEOUT"
Could you try increase the value and see if the issue will be solved or not?
#define DEFAULT_SOCKET_READ_TIMEOUT 100