geth.log is 84.73GB, so that mobile phone complains no disk space left. Would the geth.log be mandatory to generate?
Geth client doesn't generate log by default, but you could save logs to a file if you want so which isn't really useful I think.
The size of a fast node is already near 130 Gb to be sync with the Ethereum network
No, it is not mandatory to write log, moreover there is no log file by default.