Cannot start C-lightning after reboot
The first line is normal behaviour:
UNUSUAL plugin-bcli: Could not connect to 'lightning-rpc': Connection refused


Your lightningd cannot start if the underlying bitcoind is not up-to-date:
2020-07-20T02:59:44.730Z UNUSUAL lightningd: Waiting for initial block download (this can take a while!)
2020-07-20T02:59:44.732Z UNUSUAL lightningd: Unable to estimate opening fees
...
2020-07-20T02:59:44.732Z UNUSUAL lightningd: Unable to estimate max_acceptable fees

You just need to wait for bitcoind to finish IBD. lightningd will regularly poll it and launch as soon as it's synced.