The way alot, aswell and noone are combining is expected given how many other words we don't bat an eye at went the same way. "another" is the perfect example, it's just "an other" combined.
It's sort of the reverse of what happened to words like apron and newt.
The division and bracketing of phrases changes over time.
"An apron" is the modern usage of the word "napron", and a newt was originally called an eute. The grammatical need for "a" and/or "an" resulted in the root word being rebracketed and changed.
I recall "noone" being taught as acceptable by my english teacher back in 2004. That being said, she's also said some things that ended up being very wrong
it's all just made up. you can see old writings without spacing. or punctuation. you can't even define what's really a word universally. people just decided what's what and standardized it at one point just for some consistency. that doesn't mean things won't change; they most definitely will.
Ampersand is another good example. "&" was considered the last letter of the alphabet for a while. Schoolchildren would recite the alphabet and finish it with the phrase "and, per se and" ("and, meaning and").
The words got mashed together over time and the word "ampersand" was born.
The spelling differences are actually mostly due to Noah Webster standardising what he saw as pure Anglo-Saxon English without corruption by French princelings.
England and all its former colonies (except the American ones) agree on the language, and the only odd one out - the United States feels it is unique among former colonies and its parent nation as the sole owner of the most correct version of English.
I feel like that sort of misses the point. That really has to do with how we transcribe verbal speech into written. "A lot" is absolutely a phrase, I don't imagine you'd disagree with that.
That has to do with the definition of what a word even is (an open problem!). "Alot" is clearly made up of two separate units, but so is "anyway". I think a lot of people don't like this one because it's simply unnecessary. You need "anyway" to show that the two words are not stressed separately, but treated as one unit, whereas with "a lot" this is already obvious ("a" is almost never stressed).
Also has to do with English spelling just being bad, generally.