If a ship sails under a flag of convenience, it is registered in a country where taxes, etc, are lower than in the country it comes from, so if someone does something under a flag of convenience, they attempt to avoid regulations and taxes by a similar means.
If you up the ante, you increase the importance or value of something, especially where there's an element of risk as the term comes from gambling, where it means to increase the stake (the amount of money bet).
If someone or something is up the creek, they are in real trouble.
'Up the creek without a paddle' is an alternative, and 'up shit creek (without a paddle)' is a ruder form.
A vicious circle is a sequence of events that make each other worse- someone drinks because they are unhappy at work, then loses their job...
'Vicious cycle' is also used.
If you have to walk a fine line, you have to be very careful not to annoy or anger people or groups that are competing.
('Walk a thin line' is an alternative.)
The expression what will be will be is used to describe the notion that fate will decide the outcome of a course of events, even if action is taken to try to alter it.