For container I used a free sample compact I got from TKB Trading. You can use contact case that you don't use, empty eyeshadow compact, etc. Shallow containers will work better. Whatever you use, just make sure you wash it very clean and sanitize it with alcohol first.
In actual vintage cake mascara they include a tiny brush for applying, but I found modern mascara wand much easier to use. You can either wash clean a mascara wand from an old tube of mascara or grab some from aisle endcaps at Sephora.