Fixing crack in wall & baseboard
We have to assume that there's seasonal movement in the foundation that keeps these cracks alive. Therefore the best approach might be a flexible crack filler, such as painter's caulk (acrylic latex with silicone).

Scrape away all loose paint with a putty knife
Use a tool to gently groove the crack to remove loose material can create a cavity for caulk
Using a fine caulk tip, fill the cracks and tool it flat with a putty knife or similar
Allow to dry and repeat if shrinkage is substantial
Prime and paint