What does it mean to 'fuse' ores and why do we use alkali metals in the process?
"To fuse" is another word for "to melt" (e.g. "heat of fusion"). Specifically, if you say you want to fuse two materials, you melt them in the hope that they will mix.

In this case, you melt the carbonate, and hope that the chromite will dissolve in it. Because e.g. $\ce{Cr2O3}$ has a melting point of $\pu{2435 °C}$, chromite ($\ce{Fe(II)Cr2O4}$) typically around $\pu{2140 °C}$. That is out of reach with a common Bunsen burner, and even if you did reach it, it would still be the same insoluble mess after cooling down.

When your chromite is dissolved in alkali carbonate, the mixture easily dissolves in $\ce{HCl}$, and you can properly run your wet analytics.

Soldering for example is a very similar process: Your soldering iron cannot nearly melt copper, but the molten tin/lead/etc. fuses (partly dissolves/melts) with the copper surface, and you get a continous metallic connection.