It's called the DMG, and it has guidelines for creating balanced playable races for players of any type of creature. It's 5th edition ^.^
It's interesting that you'll speak upwardly of 3.5 for giving the GM power and flexibility over everything... but you insist on bashing 5e for literally doing the exact same thing, Veronica. You clearly have an issue with 5e (and that's fine! It's not for everyone!), but you aren't articulating it well - you're just taking every opportunity to make functionally baseless or intellectually dishonest jabs and barbs at the system, or insult it without backing up what your saying except with cherry-pciked bits and pieces that ignore the sections that illustrate your dishonesty.
Maybe it's not intentional... but it looks intentional right now.
To the original questions:
In 5e at least, story and background trumps hard rules in terms of where your character comes from and what kind of training they have. It's left predominately in the hands of you and your DM to decide what works ad makes sense for you. You might play a middle-aged and fairly grizzled former watchman who is striking out on adventure or is dedicating themselves to a greater oath of righteousness now - their history is the explanation for their above-commoner level capabilities and experience. OR, you might be playing a seventeen year old halfling girl who ran away from home to see the world, and has only recently discovered the beginning blooms of the kinds of magical power her music, song and dance can evoke if she puts her heart into it... Your exact amount of experience in an adventuring lifestyle is almost entirely between you and your DM. the game rules give you as et of proficiencies and skills to represent your beginning point as an adventurer, but you can decide with your DM how you came by them, or even if you have access to all of that right away, if you want.
Multi-classing has some further guidelines and rules for it in the handbook - most importantly, you don't get everything from the new class as though you'd started a level 1 character, because, presumably, you don't have the same background and training or history to explain a full initial class. Instead, you get a small subset of class-related extras along with your 1st level abilities for the new class - you might gain one extra skill, or prociciency in a type of armour you weren't good with before - but you wont' get three new skills, armour proficiency, weapon proficiency and saving throws. Beyond that, Multiclassing also has some simple strictures and requirements; in order to class into anew class, you have to meet some minimum ability score thresholds, which you don't need to meet for your first class; this mostly represents you having sufficient natural aptitude for the new skill set to jump into it at an accelerated rate, without the background training or build up that you might have had for your first class.
In terms of multi-classing access and training, again, this is something that is largely in the hands of you and your DM: you DM might ask you for a justification for your multiclass, or an explanation of why and how you're picking up this skill set now, or they may suggest multi-class options to you based on actions and focuses that your character has been displaying. They also might not, and if no-one at the table feels it's strictly necessary so long as you meet the ability score requirements then that's what works for that table. Usually, when training is brouht up in a multi-classing situation, the training is treated as an on-the-job kind of deal, rather than breaking from the game - unless, of course, you level up at the same time has being given some down time, and you want to work your acquisition of anew class into that scenario. It's very varied, is the basic point ^.^
