Regarding separate lavatories: there is no way this could possibly speed things up. The ratio of male to female passengers is not always the same, so there will always be the chance of one lavatory being available while there is a queue for the other. The only reason to have separate lavatories is if they are public, with multiple sinks and stalls. If one person goes in at a time, then separation is illogical.

Regarding seats: If such a policy were to be implemented, almost all requests would be for a female seatmate, either because men enjoy their company, women want to avoid men, or because females are less likely to have broad shoulders. I would not support the option to make such a request, as others have explained.

I understand that in some cultures women cannot sit next to unrelated men, and I am fine with FAs accommodating such requests on board if it is possible and reasonable. I personally find it distasteful, but when in Rome, etc.