Running MacBook Pro without battery
I'm not here to answer if you can run it without the battery... as I have no idea.



I'd perhaps look no further than iFixit if I wanted to replace the battery myself. I'm not sure if this is your exact model, I just picked one that was close enough: https://www.ifixit.com/Guide/MacBook+Pro+15-Inch+Retina+Display+Mid+2015+Battery+Replacement/89284 

You can typically buy the parts needed for the guide straight from them.

Before you start ordering new batteries or disassembling it further... Are you super sure it's not possible for you to let Apple handle it? Many countries (as far as I know) don't have apple stores but instead, they have "Apple authorized service providers" (or whatever they are called). It would be easy to not realize that these types of places exist in some cases. Sometimes the local store that sells Apple devices can handle the repairs as well. Not always.

Unfortunately, I can't give you a direct URL to a website where you can find your nearest service location(s) (it differs from country to country), you just have to find it through this website: https://locate.apple.com/

Make sure to click the country selection button on the top right. 

The path to the right place differs from country to country, but as I think this is the longest possible path I decided to write it down:


  Each step is a new page



Click the box that says something like: "Service and Support"


It may at this point already ask you to enter a city or area code to locate the nearest service location(s).

In a grid of boxes with Apple devices choose Mac


You may then have to further select Macbook in a similar grid

In a grid of boxes with text and icons click the box that is something like "Repairs and physical damage", 
You may then get 2 options. To call the local apple call center or enter city or area code to locate the nearest service location(s). 


You may also have to enter the device serial key or login with your apple id at some point.