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A good LOR describes specific, concrete things about you that (A) make you sound smart, dedicated, responsible, and prepared for graduate work and (B) the admissions committee would not otherwise have known. If the letter just rehashes information that appears elsewhere in your application (e.g. "received good grades") or offers generic praises ("very intelligent," with no evidence cited), then it's not very helpful to the committee. It is better to have a LOR from a lesser-known writer who knows you very well and can write a detailed recommendation than one from a high-profile writer who doesn't know you well and can't say much beyond "got an A in my class." Of course if you have your pick between an unknown writer who knows you well and a famous writer who knows you equally well and is willing and able to speak highly and in detail of your qualifications/accomplishments, you should choose the famous one.

Adcoms are tired of hearing about applicants' childhood interest in their field. It's so long ago that it usually doesn't tell them anything useful.

I'm not applying, nor do I have particular insight into the personal statement, but I went there for undergrad and know the department pretty well, so you're welcome to PM me if there are any questions I might be able to answer.

I would choose A.

If you have to ask strangers on the Internet whether you qualify as Latino or not, the answer is probably not. If that were an identity you truly identified with, sincerely and independently of anything you think people will give you for it, then you would have already checked the Latino box on the form and moved on.

Who knows you better? Who is more capable of, and enthusiastic about, writing a detailed and wholehearted recommendation?

Phone them.

Maybe "grad school advice" or "grad school question" as a subject line?

Whatever you say, I would not recommend framing "working" and "academia" as mutually exclusive.

Not an expert in this field, but I strongly suspect tutoring. It's more similar to what speech-language pathologists do, and is more difficult. Anyone with at least a grade-school reading level can read to kids, and you can read on autopilot, but tutoring isn't something you can phone in, or at least not as easily. I used to tutor elementary school kids, for what it's worth, and it was hard and I sucked at it.

Evidence of your maturity, professionalism, work ethic and self-motivation, using specific examples.

Professors get requests for LoRs regularly, it's part of their job, they're used to it. It's not like you're asking them to donate a kidney. Of course it does take them significant time and effort, if they're writing a good letter, and of course you should be polite and give them plenty of time and all the information they need, and leave them room to decline, and express your gratitude if they accept, and so on. Maybe send a sample of work you did in their class to jog their memory. But, while there are plenty of things you can do wrong, there's no secret key to making someone write a good letter for you. It depends if they were genuinely impressed with you, how much time you give them, how many other letters they've already agreed to write, what's going on in their personal lives right now -- some stuff you can control and some stuff you can't.

Talk to your recommenders about it. If they really believe in you, and it sounds like they do, they can go to bat for you (for example, call up a colleague and explain that their student will be applying and is awesome but had medical problems that are now fixed).

I know at least two grad students off the top of my head in a small top-ten department who served in the Peace Corps before applying to grad school, and neither of them even had undergrad degrees in the field they were in grad school for (and it was academic grad school, not professional school). It's not unusual for students to take a couple years between undergrad and grad school, and pretty much every grad student I've ever talked to about grad school advised me to do so. You can tell your recommenders the plan, have them write the letters when you're fresh in their minds, store them with a dossier service, then update your recommenders when you get back from the Peace Corps so they can edit the letters if need be.

Transcripts (i.e. list of relevant coursework and grades)