How to express "until ~" in Chinese?
I think the problem is, you cannot expect to translate Chinese to English (or English to Chinese) literally, word-by-word. The way that a sentence is constructed is way too different in these languages that translate word-by-word would lead to all kinds of awkward situations.

In your first example,


  There is still 3 hours until the departure of the flight.


I would consider the following expressions in spoken language:

   飞机              还有  3个小时               起飞。
The flight | (is) | still 3 hours | (from) | departure.


To emphasize 3 hours:

   飞机       还有  3个小时        才         起飞。
the flight | still 3 hours | only until | take off.
 还有  3个小时      飞机           才         起飞。
still 3 hours | the flight | only until | take off.
==&gt; The plane will only take off until 3 hours later.


Note that "until" is left out or changed by reordering those elements in your original sentence.

Or if you want to make it feel like an announcement (more formal), change the word to 距离(also means "until" in some situation) will be more suitable:

 距离             飞机起飞                  还有         3个小时。
Until | the departure of the flight | there is still | 3 hours.




As for the second example, it also requires some reordering and changes to wording:


  Then until you come here I should improve my speaking skills!


 那           你下次来之前，        我  应该            多    练习。
Then | before you come next time | I should | (do) | more practice.
==&gt; Then I should practice more before you come next time.




However, it doesn't mean that you have to left out "until" every time. Consider this example:

The company was in chaos until he became the manager.


Including "until" here or not makes the meaning quite different:

直到他成为经理之前，公司一片混乱。
　　他成为经理之前，公司一片混乱。


You can infer from the first sentence that he is the key to the change of company. But the latter sentence could simply be a statement of fact, not necessarily credit him for the change.



So, the expression for "until" depends very much on the context IMO.