自由 and 暇: freedom of choice and available time
Distinguish freedom to choose from having available time, without mapping every sense of English free to one Japanese word.
The scope of choice
色は自由に選んでください。 asks someone to choose whichever color they like. 自由, read じゆう, indicates freedom to choose within the relevant scope.
自由な時間が一時間あります。 says that there is an hour available to use freely. It focuses on having a choice about how to spend that time.
Whether someone's schedule is open
明日の午後は暇ですか。 asks whether someone is free tomorrow afternoon. 暇, read ひま, describes being unoccupied or having time available.
忙しくて、昼食を取る暇もありませんでした。 says that the speaker was too busy even to have time for lunch. It concerns lack of time, not a prohibition on eating.
Distinguish no charge from freedom
入場は無料ですが、席を自由に選べるわけではありません。 says that admission is free of charge, but that does not mean seats can be chosen freely. Price and freedom of choice differ.
When asking someone for time, お時間はありますか is another option. 暇ですか asks whether they are unoccupied, so choose the phrasing for the relationship and situation.
Can 自由 directly translate free when admission costs nothing?
Show the answer and why
Use 無料 for no charge. 自由 concerns freedom of choice or action; 暇 concerns available time.