Wood – Type of screw / fastener should one use to attach veneer covered particle board bookcases together

I'm with Lawrence on this, where there is blame, there is a claim. If you want to have a go at fixing however then go to a ships chandler and get a good glue from them. However, the trick is to clamp the pieces tight. I don't mean but some books on it but use something that has a vice-like grip spread over 3 or 4 inches. All that said, if this is an area not seen when draws/doors are closed then "No-Nails" type compound will suffice. Good luck

You have to remove the plaster & lathe to do "backer boards" as they go between the studs & are typically 2x4's or 2x6's. If you're leaving the plaster & lathe then you're talking more about a Ledger or Hanging Board that gets screwed to the studs & just sits on the face of the lathed plaster.

These are typically just 1x6's or 3/4" plywood strips & should be shimmed to straighten & flatten the wall for the cabinets. You'll need to fill the end cabinets' gaps if using this method or skin the cabinet sides & scribe those to the wall.

However, you really shouldn't need either & you should be able to hit 2 studs for each larger cabinet's top & bottom. Use Beefy Coarse Thread Deck or Wood Screws, not drywall screws. In the case of small 12" wide type cabinets, they will be screwed to the bigger cabinets & supported solely by them.

Molly bolts, Mushroom-Heads or Spreading Anchors can be used just to suck them against the wall. Screw everything loosely to start with & then shim the cabinets to perfection beside the screws before sinking them. Use an impact driver if possible, this will sink the screws better & avoid chewing up screw heads.