1) You might say, "You should practise what you preach". In AmEng, "practice".
2) I can't think of an idiom to match exactly what you describe. Such things are sometimes called "internal machinations".
There is a term commonly used in Australia to mean the undermining or weakening of an organization by insiders – "white-anting".
It refers, of course, to the eating away of the insides of wooden objects and structures by white ants (termites).
"Years of persistent white-anting contributed to the Labor Party's loss at the recent elections".