When proxy cache full it will delete the old records to accomodate new ones.
You can delete the cache from the GUI -> Security Services -> Web Proxy -> click on Clear cache button.
Regarding the logs, not sure understand you correctly.
Basically you can configure the logs in the System Administration -> Log Subscription -> select the logs.
Then from there you can set how many max files to store the logs locally and what is the max size per log for the rollover.
Or from that page you can set to send the saved log files to remote site (either remote FTP, SCP or syslog server).