You are right, for awhile is incorrect. while is a noun, so it needs a preposition to attach it to a verb, but awhile is an adverb, so it doesn't need a preposition.
Merriam-Webster has this to say about it:
Can awhile be used after a preposition?: Usage Guide
Although considered a solecism by many commentators, awhile, like several other adverbs of time and place, is often used as the object of a preposition.
… would be generous enough to let me explore their world for awhile. — David Yeadon
This Ngram graph shows that awhile was as common in the UK as in the US a hundred years ago, but since 1960 it has declined in the UK but increased in the US. for awhile is currently a lot more common in American English than British English, but this may simply be because awhile is generally more common in the US.
Combining words that traditionally were separate is more common in American English, for example anymore. As this Ngram graph shows, the usage in both countries has increased dramatically since 1960.
I have also seen alot (meaning a lot) in private correspondence, but cannot find any reference to this in UK or US dictionaries.