I just use a cheap Stanley one from Screwfix. It goes into the majority of walls. Really solid ones it may not go all the way but just tap them in with a hammer
You've got 2 options really, say you've quoted for standard way of finishing angles which is with beads as it was never mentioned so that's how it's being done.
Or send another quote with extra labour on with a disclaimer you've never done it before and may need sanding down after and you can't...
Don't think it matters what pattern artex is you, I can't see how anyone can get a good finish skimming straight over first coat. It'll be all pitted when you look closely at it
Out of interest have you just started out? As I can't see how any plasterer would second coat on top of a sloping wet first coat or why anyone would need to do 3 coats