We've long ago stopped providing a local URL Filtering database, instead opting for an on-demand lookup.
That means any update are immediately reflected on the gateways.
To check the categorization of a URL: https://usercenter.checkpoint.com/ucapps/urlcat/
Note this only applies to how something is categorized in URL Filtering and does not apply for Threat Prevention, which may categorize a site differently.
Assuming this is a non-transparent (i.e. explicit) proxy, you would need to allow the proxy IP in your Access Policy.
This presumes you do not want to enforce your access policy based on specific user/group, otherwise you'll need XFF enabled.