I've hidden all the answers and explanations in the source, for those who want guidance on crypticity.

Paying guest loses a fringe (6)
Vermin back in best Armenian families (4)
Mates in turmoil giving off vapour (5)
Tune on the radio ? (3)
WHERE THE EXECUTIONER'S AXE FALLS ? (5,7)
Food comes back as American time period (7)
Born in Little Rock, Arkansas - grew up in Colorado ! (7)
Darn fire is rubbish - more heat than light ! (5-3)

Cheers Blob. The mystery of No 7 is revealed at last.

I'm not convinced about the soundness of either no 5 or 7 - unless I'm being really dense. Is the second word of 5 clued by anything other than the orthography? Also the 5th word of 7 is not just redundant but destroys the clue.

[rab] By orthography I take it you are referring to the capitalization, in which case, yep, that is the main clue - and is pretty much an accepted method of cluing - as is using punctuation in non-standard ways. The wording of the clue of course refers to the thing that the axeman's victim's head rests upon.
Arkansas ? What's wrong with that - that's where Little Rock is.

[Blob] Well... the executioner is probably a matter of taste - I take the view that you notionally downcase and depunctuate the clue so that what's left tells you what to do. Others disagree, suggesting that if you use 'Bath' in the middle of a clue, it would have to refer to the city as opposed to 'bath' which is a tub. The only way to properly introduce ambiguity is to use it at the start of a sentence. But I'm not that extreme.

On the other hand the Arkansas clue breaks at least two rules. Firstly the definition is not "Little Rock, Arkansas grew up" but simply "Little Rock grew up". And then, if we're being pedantic (which we are), it really ought to be "Little Rock grown up". The second rule is that the definition should never come in the middle of the clue, always at the start or the end.

Everyone has their own stance on what is acceptable and what is not. I consider myself a moderate compared to Ximineans like Don Manley (whose Crossword Manual is well worth a read). However, you might consider me onerously fascist for these opinions.

I entirely agree that the definition must be either at the beginning or the end, not in the middle - but I was referring to the place Boulder, in Colorado ... so "in Colorado" is at the end as required. The Little Rock growing up was the cryptic clue, and the Arkansas for completeness, suggesting a place to be looked for. Even if you objected to this inclusion, spurious words are allowed if they do not fundamentally change the meaning, and I don't think it does.

[rab]I presume you now get the "capital" part of No.5 - as in death (literally head removal).