Hi Naneh, Yes you can buy property here. It looks like you are already in Arizona. If you are a permanent resident with a valid green card, there are no restrictions on buying or selling, as long as you are still in the USA at the time you sell.
If you are not a permanent resident, buying is easy, but when you sell there is a tax called FIRPTA that is based on the sale price. This is based on the assumption that you are leaving the country, and would otherwise not have to pay taxes that and American would have to pay, such as capital gains. The way to make this easiest is to apply for a Tax Identification Number well before you plan to sell the property. I have gone through this with past clients, and without the Tax Identification Number (or TIN) it can be complicated and frustrating.
If you are planning to rent the property, you will have to report the income to the IRS, and pay taxes on your net income. I strongly suggest you talk with a financial advisor before you take this step, since I don't know what laws there may be in Armenia that could also affect you.
If I can help you any further, please email or call me. Best of luck.
Ann Griffin, REALTOR, ABR, E-PRO, SRES
Coldwell Banker Trails and Paths
2913 N. Power Rd., Suite 101
Mesa, AZ 85215