Is it permissible for me to give Zakat on wealth, and if so, from where should I give it, knowing that I own money in my home country and I have been an expatriate and unemployed for four months now?

The basic principle is that zakat follows the money and is distributed in its location. So, if the money reaches the nisab (minimum threshold) and a full year passes, zakat becomes obligatory. The muzakki (person obligated to pay zakat) should appoint someone to disburse it in the country where the money is located, to avoid the dispute of those who prohibited its transfer. If he is unable to appoint an agent, and he has money with which he can pay the zakat in his current country, then it is obligatory to pay it, because the preponderant opinion is the permissibility of transferring zakat for a benefit, and because paying it outside its country is better than not paying it at all. However, if he does not have money to pay it, the obligation remains due upon him until he is able to do so. Then, he must pay the zakat for all the preceding years, because the ability to pay is not a condition for the obligation of zakat, but rather for its disbursement.