Point 1: There's a lot of resources online that back this up, didn't see anything refuting it. Someone might try to disqualify it because California isn't all by itself an actual nation, but that seems like an exercise in "no true Scotsman". [theguardian.com]

Point 2: In a dollar-for-dollar comparison, not true. In 2016 CA is more in the middle of the range.
[governing.com]

Once you start adjusting for cost of living and other factors, and bump the year up to 2017, it's closer to true as CA falls, according to one source, down to 41st in the rankings, not 43. Other sources (the one hosting your picture) for the 2013-2014 years ranked CA at 46th.
[politifact.com]

Point 3 Source A has the CA ranked as #2 as of 2015
[justnet.org]
Source B backs up NY outspending CA per prisoner. This can be a volatile figure, considering CA spends more than twice as much on prisons overall as NY does.
[cheatsheet.com]

Side issues: CA's spending on prisons has tripled since 1970
[politifact.com]

CA and NY have the widest gap between per-student spending and per-inmate spending:
[money.cnn.com]

Welcome to the group. Well done for reaching out to a fact finding group. What is your best method so far