1. When is the day I can get it reissued the fastest? ✔

​   When's the soonest it can be reissued?

2. Call me as soon as you're ready. ✔

​     Please call me as soon as it's available.

=> Another way: Your sentences are okay and these are another way of saying it.

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3. I have to leave this country next week. ✔

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