Is a 60Ah battery enough for a small car, and can it be done same day?

My Kia Picanto has been giving me trouble for about a week, and this morning in the DIFC parking it did not start at all, just a quiet click. A guy from the building gave me a jump, but I need the car tomorrow for work, so I cannot wait around. A friend told me a 60Ah is the right size for small cars like mine, and that some places can change it on the same day. I looked online for a Same-day Varta 60Ah battery replacement in DIFC, but every page just said fast and cheap, so I could not tell what is real. My car is six years old and has no fancy extras, just the radio and a phone charger. So I have a few simple questions. How do I know if 60Ah is the right size for my car, and is it written on the old battery? If I go to a shop in the morning, can they really finish it before lunch, or do they need to order it first? Also, do they test the old battery first, or do they just sell me a new one? I also wonder about the date on the new battery. Where do I find it, and how old is too old? Another thing is the warranty. Is a receipt enough if something goes wrong later? And does the car need a reset after fitting, or is that only for newer models? Last thing, if the car still starts slowly after the swap, could it be the alternator and not the battery? If you changed a small car battery near here, please tell me how long it took, what you paid, and what you would do differently. Easy answers help me most.