Pebbledash

I would remove any coating outside as it's prone to cracking and letting water in. Sometimes rendering isn't the answer let the building breath and repoint with lime

Yes provided that the sub base is sound

Yes providing the pebble dash is solid you can render grip pebbledash and go over it with suitable base coat and mesh

Even if it is sound, I would do a pull test first This is a piece of scrim fixed with base coat onto the wall and let dry. Next day try to pull the scrim off, if the dash comes with it then, you’ve got your answer If that works then, pin and scrim the mesh and follow up with the right procedures (prime, base, etc..)

If the render is sound yes you can re - render over as the dash will give a very good key for the new render as long as prepared properly- note : anyone who has solid render and decides to remove - can actually cause more damage to the sub base in some cases so worth baring in mind.

Mash over the top of it. Scrape any excess off. Scrim it.