Hi Phoebe!
As you seem to already know, stage dooring before a show is not really a good time. Plenty of performers will NOT sign you, but of course there's usually a few that will. (Plenty don't because they know you're not seeing the show, or rather assuming

, so if you are, tell them "good luck" or "break a leg" at the show/etc.)
It's almost universally customery to walk into the box office location and see the board of performers (if you haven't taken note to it before). Such as this may read:
" Woman in White
A New Musical
at the Palace Theatre
Starring (in order of appearance):
Marian - Maria Friedman
Count Fosco - Michael Ball
Walter Hartright - U / S Adrian der Gregorian
Laura Fairlie - Jill Paice
Sir Percival Glyde - Oliver Darley
ENSEMBLE:
"
So even if you're not buying/picking up tickets, that will be your source to see whose on /etc.
I don't really know about buying merchandise before the show - something you'll have to call / walk into the box office and inquierer about!
Best of luck! Hopefully someone else can help you too!
(Maybe check out the 'In Person' part of this forum and say "Request/Help - Oliver! West End")