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I've got several at the top of the grid that I cannot yet see. Here's a few of them:-
6 Across - "Maybe US criminals had briefly to be imprisoned"
(Answer appears to be PERHAPS which probably consists of "HA" insides of "PERPS". Is the latter word one that means "criminals"?
9 Down:- "Shame about horrible noise in tank" (7) --L -D-N This looks like being "SALADIN" ("ALAS" backwards + DIN) but I cannot see where
"tank" comes in.
18 Across - "Relaxed, one's agent finally very adequate" (12). I have
--T-----T--- and that's it!

PERPS is a US contraction of "perpatrators", so criminals.
Is SALADIN a class of tank?

18 Satisfactory, adequate.

Sat I's Factor Y

(the Y is 'Very finally', last letter).

Yes it is
https://en.wikipedia.org/wiki/Alvis_Saladin#:~:text=The%20FV601%20Saladin%20is%20a,had%20a%20crew%20of%20three.
Type - perpEtrators

Many thanks Chris E and Malone. I'd never heard of those particular tanks. I guessed that "perps" was probably an abbreviation for "perpetrators", but couldn't find a reference to it anywhere.

Rocketman, glad we could help. 'Perps' is used quite often in US dramas such as 'Law And Order'.

Thanks, Malone. Do you happen to know the parsing for these?
6Down - "City in revolution at first pretty backward, rejecting both sides.^ PETROGRAD
11 Down - "Serious wizard in Tyrone, say, worshipped figure."
GRAVEN IMAGE

Rocketman, 11 is Grave, serious, NI, northern Ireland, Tyrone say + Mage, wizard.

6 Retrograde = pretty backward. Drop both sides = drop the first and last letters, so 'etrograd', add P, at first pretty.

Sorry, Rocketman - I inadvertently typed 'pretty backward', it should just have been 'backward'.