Macbook pro retina - replaced battery quality and age?

Question

This question is about a Retina MacBook Pro, 15-inch, Early 2013 (MacBookPro10,1). It was originally purchased in April 2013.
I would like to find information about the manufacture dates of batteries, and Apple's policies for hardware repairs and refurbished batteries.
My macbook has just undergone a major surgery (at a certified Apple Support Center) after I spilled coffee over the keyboard.
The logic board was replaced (which includes CPU, GPUs, memory, etc), and so was the the "top case" block.
The "top case", I found, it a unique component that comprises the keyboard, the trackpad and the battery.
I was told that these new components are (generally) refurbished parts provided by Apple, and that support centers don't have any control over their state (new or refurbished).
Now that I have got my macbook back, however, I inspected the system to verify the state of the new components, using a combination of tools and terminal commands.
I am very disappointed to see that I've got a very old battery, as its manufacture date is 2012-07-31 (according to this tool).
Is it ok? It looks like it was a battery used in a previous generation of the macbook pro. Or is it normal that early 2013 Macbook pros had their batteries manufactured in the summer of 2012?
The battery doesn't even seem to perform correctly (or, if it's not the battery, it's the logicboard). I've tried to discharge it completely and then recharge it, but the computer shut down when the battery was just at 18%, with no warning dialog from the OS. I plugged the power cord and resumed my session on the computer, and the battery level appeared to be 16%. I charged it until it reached 19%, unplugged the cord... and the battery level jumped to 25%!
The computer computer then shut down again when the battery reached 17%. I recharged it fully, and now I'm trying again (seems to be behaving more normally, now).
Still, that's odd. The original battery never did anything like that.
If it can be useful, this is my System Monitor App battery report (not charging at the moment, 12% left):
Battery Information:
  Model Information:
    Serial Number:      D86230735FLDNMGAY
    Manufacturer:       SMP
    Device Name:        bq20z451
    Pack Lot Code:      0
    PCB Lot Code:       0
    Firmware Version:   511
    Hardware Revision:  3
    Cell Revision:      1150
  Charge Information:
    Charge Remaining (mAh):      1122
    Fully Charged:               No
    Charging:                    No
    Full Charge Capacity (mAh):  8487
  Health Information:
    Cycle Count:      3
    Condition:        Normal
  Battery Installed:   Yes
  Amperage (mA):       -2195
  Voltage (mV):        10617

Answer 1

Today I brought the macbook back to the service center, where they re-executed the hardware test.
They showed me the resulting graph, that showed that my battery state is "optimal": it was represented as a dot in the top-left corner of the green area, as in this image.
And yet, even though the problem described in the opening post hasn't happened again, I can tell that the battery lasts way less that the old one.
Again, does anyone have any information about the "normal" manufacture dates of macbook batteries?
Is it possible that this battery was designed for a previous generation of macbook pros?