Can a weapon be an arcane focus?

An arcane staff focus resembles a quarterstaff so it can be used as an improvised weapon with the same stats as a quarterstaff. Here’s the relevant rule from the PHB page 147: In many cases, an improvised weapon is similar to an actual weapon and can be treated as such.

Can I use a ring as an arcane focus?

The effect of an arcane focus is that you may use it in place of most material components, but to supply them for a spell requires a free hand to manipulate them anyway. You would just be going from needing a hand for the components to needing a hand for the focus, be it wand, pendant, or even ring.