よろしく is literally the adverbial form of よろしい, which in turn is the humble form of よい - 'good', so we literally translate it as 'well' or 'nicely'. However, よろしく is often used as an abbreviation of よろしくおねがいします, which you've already learned, but it's tricky because it can mean a lot of different things depending on the context. It can mean "please be nice to me", or "warmest regards", or "thanks in advance", etc. Because it's so often used in greetings, it can also just be used as a general greeting by itself, but it can also be used as kind of a signal that the pleasantries are over and it's time to get to work.
So, in this case, the speaker isn't saying what they want the other person to do about the 逆襲 (ぎゃくしゅう - "counter-attack"). I haven't seen the show so I don't know if there's any context, but I assume that the other person already knows what to do about it, and the speaker is saying "thanks in advance" for doing that thing. That doesn't really translate well into English, so it becomes "take care of..." but I'd say it has more of a sense of saying, "You know what to do". Quite often a literal translation of Japanese doesn't make much sense because context (or at least obvious context) can be omitted a lot more in Japanese than it can in English. So when we're translating into English we have to "fill in the blanks" as it were.
For "take care in future", I think a better way to say it would be お体に気を付けて（おからだ に き を つけて）. If you're only a week or so in, the grammar behind that might be a bit more advanced, but generally 気を付けて means "please be careful" and お体 means 'yourself', so it's works out to "please take care of yourself". (Actually 気を付けて literally means "please attach your mind" and お体 literally means "your body", but we interpret them as "be careful" and 'yourself' respectively.)
I'm not sure of any resources that specifically cover things like this. The best advice I can give is to keep at it. The more Japanese you learn, the less reliant you'll become on trying to figure out what something means in English, and the more you'll focus on what it means in Japanese. The thing about Japanese is that, compared to other languages (especially English), and despite the omission of context, it's actually a remarkably consistent and logical language - once you've got a handle on how it works, there really are very few exceptions. However, it is also quite a unique language (linguists aren't even sure what language family it belongs to), so finding points it has in common with other languages is often difficult. You'll probably more than once hear advice to "think in Japanese". That's hard when you don't know much Japanese, and it seems nonsense to suggest that you have to be fluent in Japanese in order to learn Japanese, but that's not what it means. What it really means is that Japanese is unique enough that you really have to approach it on its own terms rather than trying to match it up to another language. What I find helpful with that is in fact the approach I used with よろしく above: just a shift in the focus of the questions I'm asking. Instead of asking, "what does this mean in English?", I ask "why did they say this?"
(Mind you, right now I'm focusing on learning kanji, and I sometimes find it difficult to give the English meaning of a kanji I've learned because that means I have to stop "thinking in Japanese". I know what it means; I just have to force myself to remember what it means in English. But I'm bad at multitasking, so maybe that's it.)