> Would it be ok to ask how you're knowledgeable about this?

When I was around 6, I resolved not to become one of those rubbish adults who doesn't know anything but thinks they do: since then, I've been paying attention. Apparently, most people don't know how to do that. (Having direct experience to pay attention to probably helps as well.)

I used to use myself as a baseline for my observations, rather than the less-variable "reference adult" I now use, so my understanding of children younger than 7 is not as good as I'd like.

> so that we can hopefully learn strategies to help him live a happier life.

There's no need to wait for a diagnosis for this: this stuff is well-documented online, and none of it is that hard, even if some allistics find it unintuitive. Don't get too attached to the idea that your kid is autistic, though: use what helps and discard what doesn't, because you never know. (Do not subject your kid to ABA, and never do anything that funnels money to fake, anti-charities like Autism Speaks,[8–10] but apart from that, go wild.)

I've provided some suggestions, in case you find that useful.

> Loud sounds, any cold sensations, etc all bothered him extremely. […] He still can't walk on cold floors barefoot.

Don't try to force him into uncomfortable sensory environments. Sensory issues can manifest as mere unpleasantness, or as actual pain, so either it'd just be torturing him, or it'd train the instinct to avoid unpleasant stimuli out of him: neither of these are good outcomes. (The latter can be really hard to deal with, later in life: for example, on out-of-routine days, I still have issues connecting "my hunger pains are starting to interfere with fluid movement" and "maybe I should have breakfast then, since it is 8pm".)

If he's getting better at dealing with barriers that prevent him from doing things he wants to do (e.g. deciding to tolerate the screaming of other children in order to play on the bouncy castle, stopping once the trade-off is no longer worth it), great! Keep doing whatever's helping him develop that skill. But if he's getting better at "dealing with" uncomfortable environments by internalising that his comfort is less important than other people's convenience, that's not so great – and it's something that loving parents can easily encourage by accident. I'm not sure how to distinguish between the two, but talking might help; and, as a parent, you can make sure you're not putting him in bad situations when you can help it. (I'd love to say "never", but parenting in an imperfect world involves trade-offs like "we have to wait quietly within the hospital" or "the school run goes past that shop with a Mosquito alarm that the owner won't turn off".)

If he gets as much practice with language as your description suggests, it might be good to start talking these issues through. Ask what sorts of things upset him, and what to do about them. The focus should be on learning how to describe and talk about issues, and finding accommodations that might mitigate the issues.

In-the-moment, you can ask what's wrong, find a possible mitigation (e.g. stepping outside for a bit), and ask if he wants to do that. In-the-moment, he might be too overwhelmed for that: see [0].

> He is extremely emotional and volatile. […] He is angry all the time. […] if he does not get something immediately, then the extreme anger and breakdown occurs.

Are you sure it's anger, and not a meltdown due to overwhelm? See [0]. Assuming it is anger:

There are some simplistic things you can do to deal with anger,[1] but this advice is a muddled combination of various factors. I mean, that advice works, I'm not knocking it, and it's as good a place to start as any, but you'll want to progress towards him noticing when he's getting angry, understanding why, and channelling the emotion in more fruitful directions.

Many autistic people struggle with understanding emotions, both others' and their own,[2] so talking through some algorithms to identify and respond to various internal mental states might be useful. For anger, talking about the reasons for the anger, then possible ways to resolve those situations (if actionable) or do something to calm down (if unactionable) or both (if actionable, but too upset to take the action just now), and setting simple rules like "we don't hit people / make loud noises when we're angry" ("loud noises" because shouting in anger is intimidating and can scare people: don't give any arbitrary orders about what is/isn't acceptable self-expression) can help. For frustration (i.e., when you want something to happen and it's not happening), asking about what's frustrating, commiserating, and suggesting a less frustrating thing to focus on instead, can help.

For the bike example… well, it depends on the kid, but I'd try explaining that riding a bike can take years to learn, because it's doing a lot of different things at once (balancing, pedalling, steering, going fast, looking out for obstacles), and suggesting to practice one of those individually (e.g. practising balance by trying to keep both feet off the ground for a few seconds while kicking forwards without the pedals – going as fast as possible helps), and that there are lots of ways to play with a bike, and he'll learn to ride it eventually. (He will learn to ride a bike, if he keeps at it, regardless of how bad his coordination issues. Perhaps not well enough to ride alongside road traffic, but if you can learn to walk, you can learn to cycle.)

Since he can write, he presumably reads. Perhaps he could read some books about this: Focusing by Eugene Gendlin[3] is a good one, though perhaps not that good for a 4-year-old. (You can stop worrying about this kind of age-appropriateness by age 10, though make sure at least one of his books is a big dictionary.) It's important to provide a wide variety of techniques and paradigms: no psychological models are correct, but some are useful.

Other people have provided some age-appropriate advice[4], and while it looks broadly like the right thing, I have some caveats to add. Keep in mind that many autistic people's emotion doesn't quite match your average allistic's emotion, and body language is usually quite different, too[5]. I'd be wary of telling an autistic kid what they are feeling. For unrelated reasons, saying things like "you're laughing, so you must be happy" that are not literally true is a bad idea, and might interfere with tickle consent[6]: "you're laughing, so I think you're happy" is much better wording.)