There is a bug causing a template error in 4.7.3 which, looking at your system log is an error you're encountering here. There is a fix for this in 4.7.4 which is beta right now and expected to be fully released tomorrow.
Your other issue about the updateCheck task, it appears to be timing out on your server or there is something blocking it. This is due to when executing the task manually, it is resulting in a 404 not found error on your server. Few things you will want to check:
Your server can make outbound, external connections.
If you are running mod_security, please disable this temporarily.