Hi,
I am doing a research paper on panel data taken from BRICS nations as representative of recently industrialized and emerging market developing economies . i am using stata
After declaring my dataset as panel data, I have appointed general pooled ols model to do the regression which gave me R-squared as only 0.7421. intuiting it as not sufficient i went to fixed effect(fe) model, but it further reduced my (overall) R-squared to 0.1251 . then, i did random effect (re) model which gave (overall) R-squared as 0.7421. then, i did hausman test to choose between fe and re, which gave chi-squared as negative to be -205.32 and thus, hausman failed

My questions:
Q.1) how to choose between pooled ols and fixed effect? Please describe command too, if possible.
Q.2) as hausman test failed, how can i choose between fe and re? Please describe command too, if possible.
Q3) does any other model exist that can be used for panel regression other than pooled ols, fe and re in general? does any of them can be used for my study? If yes, how to choose between them?
Q.3) what kind of other test can i employ in my study to check characteristics of my data?
Q4) does things like heteroscedasticity, unit root test, autocorrelation etc creates a problem in panel data? if it does, how can i check them?
Q.5) any other suggestion for my study is extremely appreciated

thank you for any and all kind of help that canbe provided for the study.

Ps. please excuse my poor knowledge about econometrics. please answer as soon as possible as i have a close deadline to submit my work