They are both right but have different meanings.
It doesn't matter anyway, you can do it any way you like.
Yes, anyway is a compound word. any + way = anyway Both "any" and "way" are words on their own. So, when you put them together, you get a compound word.
anyway
Yes, if used in the right context, it is a word.For example, "where is Sarah anyway?". And "well, I had things to do anyway". Are the correct use.While "is there anyway I can find out who the caller is?", is incorrect, while "is there any way I can find out who the caller is", is correct.
come what may, anyhow, regardless, by hook or by crook, anyway, in any case
You would use the two separate words "any way" ONLY to indicate that alternate means or modes are acceptable. "You can do this assignment (in) any way you choose." But the adverb "anyway" indicates an inevitable conclusion regardless of the means of attempt. "We were going to do the assignment anyway." The confusion may arise from their use in motive travel or in steps to a process. For example "We couldn''t get there any way." "We couldn't get there anyway." In the first case a preposition "in" or "by" is omitted and the word "any" is used to mean "none of the many possible". In the second, "anyway" substitutes for "regardless".*The stand-alone interjection is simply a segue from one idea to another, ending the original topic and moving to another, and is almost always conversational. "Anyway, I have to get back to work."
No, anyway is an adverb. It can mean "in any manner possible," or "in any case," or nevertheless (regardless).* if the term follows a preposition, it is the two-word noun phrase any way.
nope. Not that I know of anyway
Any way you like, you'll wake up soon anyway.
When encountering any pedestrian, you should give them the right-of-way.
There is no way to get illegally married and then acquire any of the legal rights of marriage.
If there is any doubt about who has the right-of-way, it is best to yield to the other driver to avoid a potential collision.