The answer seems to be pretty clear from the Wikipedia entry on Lin Biao.
how did he get any power at all?
I am quoting the same article here:
As a child, Lin was much more interested in participating in student movements than in pursuing his formal education. Lin joined a satellite organization of the Communist Youth League before he graduated high school in 1925. Later in 1925 he participated in the May Thirtieth Movement and enrolled in the newly established Whampoa Military Academy in Guangzhou (Source: Leung 69)
This is shows his innate revolutionary nature to participate into community based movements.
How did he meet with Mao?
Support from Mao's Wiki
Hiding in Shanghai, the CPC Central Committee expelled Mao from their
ranks and from the Hunan Provincial Committee, punishment for his
"military opportunism", for his focus on rural activity, and for being
too lenient with "bad gentry". Source: Wiki of Mao
Wandering the countryside, Mao's forces came across a CPC regiment led
by General Zhu De and Lin Biao; they united, attempting to retake
Jinggangshan. Source: Wiki of Mao
Returning to Lin's page,
After joining forces with Mao, Lin became one of Mao's closest
Source: Mackerras, McMillen, and Watson. 140
Why did Lin choose to be close with Mao?
During the Jiangxi Soviet and Long March period, Lin, despite his
youth, established himself as one of the CCP’s leading military
tacticians and battlefield commanders. He became closely aligned with
Mao and praised him both in public and in writing; whether this was
sincere or a tactical career move is unknown. - See more at:
Well, I couldn't find a definitive proof, my take would be that his nature to revolt made him take sides with Mao and ended up getting trapped in a game of political power!
So, yes, later he realised his initial mistake and it was too late to step out of it, his request to cancel his appointment as the Vice-Chairman was rejected.
Source: Qiu The Culture of Power. 78-79
How he rose to power:
You can refer to the section Rise to prominence in Lin Biao's Wiki which describes various incidents where Mao makes preparation to ensure Lin is raised in the chain of command the most significant one being Mao's decision to make him the Vice chairman.
Yes, the account says he was diagnosed with mental illness only by 1953, by the time Mao has complete faith in him.
In early October 1950, Peng Dehuai was named commander of the Chinese
forces bound for Korea, and Lin went to the Soviet Union for medical
treatment. Lin flew to the Soviet Union with Zhou Enlai and
participated in negotiations with Joseph Stalin concerning Soviet
support for China's intervention, indicating that Mao retained his
trust in Lin.
for more refer to Alliance with Mao section.
A possible explanation for him acting like a psychological basket case (I assume it means psycho :P) other than his mental illness could be:
Because Lin had no real interest in the position of Vice-Chairman, he
did little other than whatever he believed would ingratiate himself to
Mao. Privately, Lin had no interest in promoting the Cultural
Revolution, and attended government meetings only when Mao demanded
that he do so. Those colleagues closest to Lin noted that Lin avoided
talking about the Cultural Revolution in any context other than public
speeches, and when pressed would only make very brief and ambiguous
statements. After 1966, Lin made no phone calls, received few
visitors, secluded himself from his colleagues, and gained a
reputation as being "reticent and mysterious". He did not take an
active role in government, but allowed his secretaries to read short
summaries of selected documents for half an hour in the morning and
half an hour in the afternoon. This was generally insufficient to
fulfill the responsibilities of vice-chairman, and he left most
important work and family duties to his wife, Ye Qun.
Refer Activities section for more.
I hope this answers your question of a mentally unstable soldier rising to be secon-in-command of the Chairman Mao.