Foreign students are entitled for discounts just like local students are. They should only present their passport instead of an ID.
Veterans are not entitled of double discounts. You can decide between a student discount for your property tax, or the veteran exempt of property tax payments for the first four months, only for a property up to 70 Squared Meters. You are entitled only for one of those discounts, and in accordance with your holding of the property.
Yes, so long as the property is clear of debts. To pursue a transfer of ownership of a property, you should bring a selling agreement, the ID of both parties and a power of attorney form of both sides.
In order to cancel your registration as a resident of your apartment, you have to inform the municipality on the date of departure by mail, or transfer a hand written approval of the landlord which declares your departure, which includes the date of departures and a copy of the landlord's ID.
If it is only one payroll that is too high for a discount, you may still be entitled of a discount. The calculation of your payroll will be the average of your last 3 payrolls, so if one of the payrolls is high it can still be okay in the sum up of the 3 months.
If the owner lives in the property, they are considered as the only holders of the property. The other residents are considered secondary residents and will not be registered in the municipality. You can still ask for a regular discount due to low income. In this case, the discount will be given in accordance with the average payment of all the residents in the apartment.
A student thar rents one apartment but holds another one: The rent that is being payed to you will be counted as an income only if the amount that you receive as a landlord is higher than what you pay in your residential apartment. Even in this case, only the difference between the payment and the income will be counted as an income. For example, if you receive rent from your owned apartment at a rate of 2000 ₪ but you pay your residential apartment rent at a rate of 1000 ₪, it would be counted as a 1000 ₪ income.