Unless I am trying to be funny and the ambiguity of the words I choose is desirable for the humor, I try not to use ambiguous language at all.

Yes, because I am a simpleton and Fortnightly and 'twice a week' already exists.

Get out of my head

The team I was on at work number of years ago had to hash this exact thing out because we had a "biweekly" status and was confusing people. We ultimately landed on not using the term.

Bimonthly and biannually have the same problem.

There are not two definitions. The prefix (bi) modifies the root (week). The suffix (ly) modifies the combination (biweek). Biweekly will always mean "once every two weeks" due to the order in which English dictates that the modifiers operate.