1. You will have US source income relating to the rental property; you file a nonresident alien tax return using our partner Sprintax.
2. Your rental may in fact generate losses with interest expense, property taxes, and depreciation (please make sure you set the asset up correctly and calculate depreciation of the structure correctly; you do not depreciate the land value). All of this becomes important if you sell the property.
3. Your holding period of the house already exceeds a year and a day so any gain will be long term. Your foreign residency has nothing to do with the capital gain rate; the capital gain rate will be whatever Congress says it is in the year you sell it.
4. You can still buy and sell stocks in your US account; however, the brokerage will issue a Form 1099 B with your dividend and gain loss activity tied to your Social Security Number and you may well have to report that on your Form 1040NR.
