SECP256K1 Jacobian algorithms
Looks like you found those algorithms here?


  I found out the point at infinity is (0, 1, 0), even I am not sure if this is correct.


Yes, you are incorrect about the point at infinity in Jacobian coordinates, which is $\infty = (1:1:0)$. See the answer here for more about that. If $P_1 = -P_2$, you have $P_1 + P_2 = \infty$. 

I would highly recommend getting your formulas from the Explicit-Formulas Database in the future, or at least using it as a cross-check. They do a great job  sourcing where their algorithms come from.