Those things are fairly easy to explain and they also aren't god-given facts.

> children never have accents, and adult non-native speakers do

This mainly due to two things:

1. Language learners usually try to map the sounds they already know (from their own mother tongue) to the new language's sounds. In fact, there are studies that suggest that, depending on their mother tongue, language learners will not even notice certain differences between sounds in the target language and their native language. (Consider how Japanese people tend to have issues distinguishing the letters R and L, or how both English and Spanish native speakers usually cannot pronounce the French/German "r" properly because that sound doesn't exist in their native language.)

This is not at all set in stone, though, because it only takes a handful of weeks of focused practice to reset your ears (and your tongue) and tune them to a new language's sounds – preferably before you learn any of the vocabulary or grammar of that language.[0] Also, the greater the spectrum of sounds you already know (the more languages you speak), the easier it will be for you to learn a new language's accent as your brain will be already attuned to listening closely to tiny differences in sound and speech melody.

Once again, consider that a child has years to learn the sounds and all these nuances.

2. Habits. Language classes almost never focus on pronunciation and speech melody in the beginning. From my POV this is a huge mistake as it means that language learners attending such classes will sooner or later get into the habit of pronouncing words of the new language using their native language sounds. That is, when they see (or think of) a word in their new language, they will no longer pause to think about how to pronounce it – they will just do it. Unfortunately, at this point it's pretty much game over as it will take a lot of work to change these habits. Then again, a lot of people also don't really care that much about having an accent.

> Another is that children do not need lessons to learn a language, and adults always do.

This is not true and I know a few people who have gone the full-immersion-zero-lesson route. It is incredibly hard, though, given the time constraints you usually have (usually a few months to a year) and you will usually progress only very slowly. Again, just consider how much time it takes a kid to learn a language by just observing and mimicking others! For adults, lessons are simply a much faster way to get started and become somewhat proficient in a language. Also, once they've taken a few lessons, they will be orders of magnitude faster at learning the rest of the language.

[0]: For an introduction to this approach of learning a language, I can recommend Gabriel Wyner's book "Fluent Forever" and, also, his pronunciation trainers and his YouTube videos on the International Phonetic Alphabet (IPA). They got me from speaking absolutely zero Spanish to being asked whether I'm a native speaker in about two months of living in Colombia. …which doesn't mean I was speaking perfect Spanish at all – but it sounded like I was! In fact, on various other occations, people told me that they could tell precisely which city I had learned Spanish in because I had become so attuned to the accent people speak there.