If I am running negative binomial regression $($NBR$)$ on SPSS$-29$ and decide to use $2$ separate independent datasets. Let$$s say I run NBR in dataset #$1($designated as training dataset$)$ and generate model, and then run NBR in dataset #$2($designated as testing dataset$)$ for external validation and use only dataset #$1$ for K$-$fold cross validation.

$1.$ For external validation, If the performance metrics $($AIC$,$ Deviance, Log Likelihood$)$ for the original dataset designated as training show small difference from testing dataset what conclusions can be drawn?

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$2.$For external validation, If the performance metrics $($AIC$,$ Deviance, Log Likelihood$)$ for the original dataset designated as training show small difference from testing dataset for one metric and large difference for another what conclusions can be drawn and how it be corrected?

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$3.$ Why do we conduct external validation?

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$4.$ For K$-$fold cross validation $(10-$fold$),$If the performance metrics $($AIC$,$ Deviance, Log Likelihood$)$ for all $10$ folds are averaged after running NBR on each, $$what conclusions can be drawn with the average and what do we compare this average with to see if difference is small or large $($in what SPSS output can I find the metric for comparison$)?$

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$5.$ For K$-$fold cross validation $(10-$fold$),$ If the performance metrics $($AIC$,$ Deviance, Log Likelihood$)$ for all $10$ folds are averaged after running NBR on each and I see that the difference is small in one and large in another, what can I do to correct this??

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$6.$ Why do we conduct K$-$fold cross validation?

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$7.$ If the training metric $($AIC$,$ Deviance, Log Likelihood$)$ is higher than testing metric what does it suggest and should I keep it or correct it$?$