A car battery warranty in the UAE usually runs 12 to 24 months, depending on the brand. A claim is accepted when the battery fails a test within the warranty period and the failure isn't caused by something outside the battery, such as a charging fault, wrong fitment or damage. Keep your invoice and note the serial number. Before you claim, have the battery and charging system tested: a battery that went flat but tests healthy is usually not a warranty case.
The exact term for your battery is stated in your quote before any work starts.
Ask which type you are getting before you buy, and whether the replacement battery restarts the warranty or continues the original one.
Many batteries brought back as faulty turn out to be flat rather than failed: something else in the car stopped them charging. That is why battery makers' testing guidance, such as GS Yuasa's, has the battery recharged and retested before it is judged. A new battery fitted to a car with a failing alternator, or with something draining it overnight, will go flat again. That is why we test the charging system as well as the battery before deciding anything. If it is a drain, read why a car battery keeps draining overnight.
Sometimes. A new car's manufacturer warranty often covers the original battery for a limited period, but usually not batteries as wear items after that. Check your car's warranty booklet or ask the dealer. A battery bought later is covered by its own battery warranty, not the car's.