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.