Gfrktyl

A single one, just to heat things up a bit:

1-2-3 is a tree I'd much prefer (to vulgar ash)

4 is actually fifth in line, the second of its kind, for me (but sixth for Cyril)

5-6-7 is 1-2-3's eastern cousin, but not as big (and much more tasty)

8-9 is trust in hospitality (stock up on it)

10-11, I'm unsure (of what to say)

If no-one gets it by tomorrow I'll drop another hint.

The 11 letter word, 'just to heat things up', is

FIREFIGHTER

a tree I'd much prefer

FIR tree

actually fifth in line, the second of its kind, for me (but sixth for Cyril)

E is 5th in the latin alphabet (and 2nd vowel), 6th in cyrillic [абвгде]

eastern cousin, but not as big (and much more tasty)

FIG tree, yum!

trust in hospitality (stock up on it)

HT ... well I just inferred it from the other clues. FIREFIG--ER. What else could the two letters be? But as to how the clue fits, I don't know. Stealing hand towels from hotels? [EDIT: using OP's hint: the stock symbol for Hospitality Trust.]

I'm unsure (of what to say)

"ER...."

The word is:

FIREFIGHTER

1-2-3 is a tree I'd much prefer (to vulgar ash)

FIR is type of tree

4 is actually fifth in line, the second of its kind, for me (but sixth for Cyril)

'E' is the fifth letter of the alphabet (i.e. "fifth in line") and the second vowel. Didn't quite get the Cyril reference (except that the name contains a 'y'?)

5-6-7 is 1-2-3's eastern cousin, but not as big (and much more tasty)

FIG is a type of fruit

8-9 is trust in hospitality (stock up on it)

HT seems to stand for "Hospitality Training" (according to the almighty Google)

10-11, I'm unsure (of what to say)

ER is the sound people generally make when they are unsure of what to say