Батя = father (colloquial, but rather common)
Деятель - literally "a prominent figure", but can be used ironically, especially about someone who's energetic but fails to produce anything except of trouble.

Филиппыч перед управой прогибается ~ Fillipych bows and scrapes before administration

Взыскание is (official) reprimand, that goes into person's file. "Неполное служебное" is shortened from "Неполное служебное соответствие", so this guy was given an official reprimand (влепить = дать /slang/) which said that he is not 100% qualified for his position because of the incident with "гаишник" (road policeman).

Еще одно взыскание и всё, на гражданку ~ One more reprimand and that's it, he is civilian. (гражданка ~ civilian life, usually as opposed to the service)

PS. Oops, I was late