It's a problem in the United States! In the United States, "fortnight" (and "fortnightly") are understood, but not used.
"Biweekly" is ambiguous and must be understood from context. It can mean either every two weeks or twice a week. I think it more often means "every two weeks." Certainly, that's what I would expect if someone said "you are paid biweekly" or "The New York Review of Books is published biweekly."
The safest thing is to say that the event happens "every other week" or "every two weeks," and people really do say this.
For something that happens twice a week the safest thing is to say "twice a week," and it is even better, if possible, to name the days of the week when it happens: "Milk is delivered on Mondays and Thursdays."
In theory, "semiweekly" means "twice a week," but almost nobody every uses it. It sounds pedantic. It doesn't clarify the situation because, since it is rarely used, people still need to ask what it means.
The same ambiguity exists with "bimonthly" (should mean every two months, often means twice a month).