Anissa being a skilled hand-to-hand combatant prior to expressing her powers fits in well with Thunder's power set. Being able to be Nigh Invulnerable by increasing her density is great for defense, but isn't as helpful for offense. On the other hand, a martial artist who can also become Nigh Invulnerable makes her an effective superheroine right from the start. Even with the show giving her Super Strength, this still gives her an advantage.
Inspector Henderson, an ally of Superman in the comics, now an antagonist in the show. It makes sense when you remember that Superman works with the law, while Black Lightning in the show is a vigilante working outside the law.
Jefferson seems remarkably unaffected whenever he hears Henderson disparage Black Lightning, not showing any anger or resentment. Episode 5 reveals why: Henderson has been Black Lightning's secret Friend on the Force and the two have cooperated in the past so Jefferson knows what Henderson is saying is what he's officially supposed to say, not necessarily what he really thinks.
Unfortunately, this working relationship might change as of "The Book of Fate", when Black Lightning was framed for killing Lady Eve.
Henderson's attitude seems more nuanced than that. There's a difference between recognizing the necessity of having Black Lightning around and liking it. And when Henderson learns that his friend Jefferson has been Black Lightning behind his back for all these years, it puts a serious strain on their relationship.
Lady Eve is a particularly nasty sort of criminal boss: since her legal job is owner of a funeral parlor, not only does she exploit the people of Freeland, she can continue to exploit black bodies even when they're dead, having been killed due to the crime she herself is responsible for.
Lynn trusting Jefferson to train Anissa (and presumably later Jennifer) in the use of their powers and enhancing their skills makes a great deal of sense, and not just because he's their father; he's not only a veteran superhero bringing his own experience to the table, he's also a literal teacher experienced in educating young people.
When he's Black Lightning, Jefferson tends to use a lot of antiquated mid-90s slang. It's not just a case of Totally Radical (though it totally is) but the fact that Jefferson probably used that kind of language when he was in his twenties and operating as Black Lightning. It's thus become part of the persona he's adopted even though he's a middle-aged man using it.
The aquatic imagery (the piranha tank, the harpoon gun) in Tobias's office clearly are meant as plays on his surname (which itself, combined with albinism and Jefferson's quest for vengeance, are almost certainly intended as Moby Dick references). However, Whale's aquatic motif, contempt for other black people and using his piranha tank as method of disposing of minions who've failed him could also be meant as a reference to black people historically being denied chances to learn how to swim, public pools being paved over after getting desegregated, and possibly even those who jumped overboard during the passage across the Atlantic.