Your walls are plaster on metal lath. The plaster scratch coat may have a relatively high cement content. I would guess 50s construction? The ideal would be to demolish the walls with mallet and pry bar, possibly upgrade insulation and electrical while walls are open, and re-apply drywall.
From your description I don't see much point to saving the old walls due to condition and inability to maintain. The texture paint is manageable and repairable. What are your ideas about major renovation as opposed to best possible repair? Does it fit your budget and tolerance for mess and inconvenience?