Macbook Pro Battery 0% and wrong date Model: MacBook Pro Retina, 13-inch, Early 2015
While I was working, I didn't realize that the battery was low and as a result, my MacBook Pro shut down when the battery had no power. So, then I plugged in the charger and powered it on. This time I noticed something was strange. The battery was stuck in 0% for like around 10 minutes and the date got reset to 1st January 2017. I tried resetting NVRAM. Nothing happened. So, then I ran diagnostics and I got this as a result:

Here's the battery information:

Here's a screenshot from Battery Health:

Now it is pretty obvious that you might ask me to change the battery because the screenshots say so, but I want a final opinion from you guys what to do next. Everything was working fine and all of a sudden this happens. I feel if I plugged the charger in time, I wouldn't have to see all this. And also a new battery isn't exactly affordable for me at the moment. And it is also important to note that while the charger is on, it shows orange LED. So, what should I do?
Your battery is dead.
You need to replace the battery.   Granted, it's a bit young at just under two years and 820 cycles, but it's not uncommon nor unheard of.  Unfortunately, batteries die for any number of factors.
With your specific battery, it appears that it won't take a charge, thus it cannot hold one.

Everything was working fine and all of a sudden this happens. I feel
if I plugged the charger in time, I wouldn't have to see all this.

There are a number of factors that contribute to premature battery death - it could have been defective from the factory or you could have subjected it to extreme conditions.  Perhaps something in between.  The point is, it happens.  There is nothing you could have done to prevent your battery from degrading.

...also a new battery isn't exactly affordable for me at the moment.
And it is also important to note that while the charger is on, it
shows orange LED. So, what should I do?

First off, the orange LED means it's sending voltage to the charging circuit or &quot;charging&quot; for short.   It doesn't mean it's &quot;successfully charging&quot; the battery.
Getting an Apple Store to change out your battery will be very expensive (minimum $500).  However, a replacement battery alone is fairly inexpensive (around $70 USD) if you are willing to change it out yourself.  ifixit.com has an excellent step-by-step guide to walk you through it.  They rank it as difficult, not because it's complex (it actually quite simple) but because the battery is glued in and you have to be careful.