I think the focus of this question is an understanding of Volkswagen part numbers.
The Volkswagen part numbering scheme is fairly straight forward to understand once you know more about it. Essentially all part numbers are in a fixed format and once you know the system, you will be able to work out which parts are interchangeable. The format is as follows;
NNN NNN NNN LLL
(N = number, L = letter)
The first the blocks of three numbers are always present, the last three letters are optional.
The number of the first block signifies the vehicle type with the second two numbers, combined with the first identify the specific model.
For example, 111 is a Type 1 (passenger car) model 11 (Standard Beetle). 190 signifies an early Mk2 Golf (or Jetta), 1J0 actually refers to a Mk4 Golf platform vehicle (i.e. Golf, Jetta, Bora, etc...). 1K0 is Mk5 and 1K5 is Mk6 (as the Mk6 acutally used a revised Mk5 platform, hence the major model letter being the same).
The first number of the second group of numbers relates to the main part category and the second two, the sub-category. The main parts categories are as follows;
2, Fuel Exhaust and Heating System
4, Front End
5, Rear Axle
6, Wheels and Brakes
7, Bumpers Levers Pedals
The final group of three numbers is the component code. The final digit of this number group is, for parts which fit a specific side of the car, always an even number when it's fitted to the right side of the vehicle and an odd number for the left hand side.
The optional letters following the part (upto a maximum of three) signify variations and updates. These always run alphabetically. These are for when there is a revision to a part or a part is superseded. A part with the same numbers but different letters will typically be interchangeable.
Lets take a look at the specifics of what you've asked;
1J0 915 105 AD
1J0 = Mk4 Golf platform. This does not mean that this is the ONLY vehicle this parts fits, just that this was the FIRST vehicle in which this part was used
915 = 9 = Electrical group. I don't have a specific list of sub-groups but I would assume 15 relates to the battery and charging system.
105 = The specific battery specification (the fact 5 is odd irrelevant as there is only one battery on the car, however the battery in a Mk4 Golf is fitted on the left hand side of the car, when viewed from sitting in the drivers seat).
AD = revision code, the original part number will have been something like 1J0 915 105 which will have been replaced with 105 A then eventually 105 AD
000 915 105 DE
000 = No vehicle code, generic part (i.e. fits any vehicle)
915 = electric group, presumably battery and charging system sub-group
105 = the specific battery specification
DE = revision code, DE alphabetically supersedes AD
In answer to your second question, I'd personally go with whatever brand I'm comfortable fitting based on the best price with a reasonable warranty period.
Your final question, I am aware that some of the Mk6 platform (1K5) cars do need their batteries coded in, this is usually restricted to the Bluemotion models as these have a sophisticated charging system which supports regenerative braking via an "intelligent" alternator. I would doubt that your car would need to be coded in and I've seen many examples of Mk5 (and some Mk6) platform owners who've replaced their battery without issue.