"Hazme caso" meaning in English?

As part of my attempt to keep my Spanish up, I read short books and articles. In a book I’m reading, one character says to another, “Hazme caso, no quiero preocuparte.” I couldn’t find “Hazme caso” in any of my dictionaries, but I read it as “Believe me…” Am I right about that? Also, is that Peninsular Spanish, or is it used in Latin America also?

I think it’s “pay attention!” (hazme: haz < hacer + me).

Both “believe me” and “pay attention” work, but in different contexts. For the OP’s case, I’d say “believe me”.

Other frequent meanings are “just do as I say” or “don’t worry about it and just follow my instructions for the time being” (tú de momento hazme caso).

I’ve heard the expression from speakers with several different dialects and nationalities including Costa Rica, Mexico and Argentina. There were dialectal variations but they were those that are general to the dialect, such as vs vos.

“My house is a hazardous waste site, amigo.”

Nono, “My MALE house is a hazardous waste site”. Can’t forget about the gender.

Apropos of nothing much, we’re watching the new season of House of Cards and some bug in the delivery system causes the Spanish subtitles to appear ONLY for written materials. A banner for “America Works” popped up the translation “AmTrab” and even my poor Spanish could appreciate the colloquial construction.

Likewise, I haven’t been able to find out what the common phrase “sin embargo” means by looking up the individual words. What does the phrase mean literally? What are the idiomatic meanings?

It’s Spanish LOLCats.

I can haz queso?

Hazme caso is written in the imperative (second person singular) form, and roughly means “pay attention to me!”, as an order. How strict or serious that order is depends on the situation. It can be anything from your teacher teaching a lesson, your superior telling you what to do for your job, to your little girl telling you to pay attention to her while she tells you about her unicorn story.

Sin embargo is used similar to the words “nevertheless” or “however”.

Embargo in this case means “obstruction” - sin embargo links two clauses or situations which are somewhat opposed, but “in this case not really”. So, as Karl Grenze says, nevertheless.

“It was a dark and stormy night…” has a tongue-in-cheek Spanish cousin: Era de noche y sin embargo llovía. Since there is no contradiction between “it was night” and “it was raining”, the sentence is completely nonsensical. It’s used to point out that somebody has just said something which makes about that much sense while being grammatically correct.

Did you guys check DRAE? I know it may seem obvious, but I know that many people tend to jump to the bilingual dictionaries for second languages; for someone whose level is high enough, a monolingual is often better.
embargo
caso (hacer caso requires scrolling down)

An expression which includes a noun will be listed under the noun.

So could hazme caso also translate as “Listen,” as in “Listen, you need to go talk to her.” ?

And, could you say, “Me crea[s]” for “Believe me” ?

It would be a tad more emphatic. As in “listen up”.

Me creas would be subjunctive, you’re looking for créeme, but hazme caso would also work. Hazme caso and its synonims are often combined, in a way in which the second sentence is an expansion of the first:

Mira, tú hazme caso. Tú escucha: créeme, haz lo que te digo y verás como sí que funciona.
Look here, you just listen to me / do as I say. Listen: believe me, do as I say and you’ll see that it works.