Thinking of buying a used Audi in Abu Dhabi, should I worry about the gearbox?

I have only been in Dubai for about five months, and this morning my Pajero refused to start in the basement parking of my building in Al Barsha. Just a weak clicking sound and then silence. A security guy helped me with a jump and it started, but he told me straight away that the battery is finished and I should change it today. Back home I would just ask my cousin who knows a mechanic, but here I don’t have that kind of connection yet. I have noticed how many places sell batteries, from big shops to small garages to guys who come on a motorbike with a battery in a box. A colleague of mine mentioned Amaron and said many people in the UAE use it, but then he also said the dealer is just as important as the brand, which honestly surprised me. I went online last night and found a page with expert tips for choosing an Amaron battery dealer in Dubai, and it talked about things like checking the date on the battery, asking for a proper warranty card, and making sure they test the old one first. I never thought about those points, so now I feel a bit lost and a bit more careful at the same time. What I want to ask is, how can a normal person like me tell if a shop is honest when I know nothing about batteries? Is it okay to ask them to show the manufacturing date, or will they find it rude? Should the warranty be written down and stamped, and what is a normal length for a battery like this? Another thing I’m curious about is the price. I got three quotes and they are all different, one very low, one in the middle, and one quite high, and none of them wanted to tell me the exact model number on the phone. Is a lower price a red flag, or is it sometimes just a smaller shop with less rent? Also, my car is a diesel and I’ve heard they need a stronger battery, so how do I make sure I’m not given the wrong size? Does the shop usually check the alternator too, or is that something I should ask for separately? I would also like to know if mobile installation is trustworthy, because it would save me a lot of time, but I don’t want to take a risk with a stranger in my parking lot. If you have changed a battery in Dubai recently, please share what you paid, how long it took, and whether you had any problems after. Even a small tip would help a lot, because I want to sort this out properly before the weekend. Thank you in advance.