Is it ok that a hot wire connects to two separate switches?
That is a perfectly functional way of splitting a single hot (highlighted green in your sketch) to supply power to two separate switched fixtures. However, most smart switches require a neutral conductor in the switch box so there can be an always-on connection for the "smart" circuitry. 

It's hard to tell whether or not you have this because all of your conductors have the same color insulation. It looks like knob and tube wiring, so there is a distinct possibility of the neutral not being present in the switch box. In older circuitry it wasn't uncommon for the installer to run hot to fixtures via one path and return the neutral to the fuse/breaker panel via a completely different route.