Is it permissible to pay off an individual's debt from zakat money, and is it permissible to give zakat in a country other than the country of work (such as Egypt instead of a Gulf country where the zakat payer works)?

You are not permitted to pay off your debt from your Zakat (definition) money because you have not spent it on its lawful recipients mentioned in verse 60 of Surat At-Tawbah (definition). As for your money on which Zakat is due, if it is from the "inward" assets (such as cash and trade goods), you must deduct your debts. If a nisab (definition) (minimum taxable amount) remains, then Zakat is obligatory on it; otherwise, it is not. Regarding the transfer of Zakat from one country to another, there is a difference of opinion on this matter, and it is more prudent to distribute it in the country where it became obligatory.