Fixie Conversion?

Well, yes-and-no ...

A "Track" bike is generally unsuitable for Road riding because the steep 74º head tube angle will make riding distances tedious -- that is, the geometry really precludes turning a "Track" bike into a "normal road bike."

Having said THAT, you could fabricate a derailleur hanger, but due to the frame's rear spacing you would be limited to using a 5-speed Freewheel (or, a vintage SunTour Ultra 6 Freewheel).

Presuming your trips are generally short & you are willing to live with the steep head tube angle AND you feel a need for more than one gear, then I think that your realistic (?) option is limited to installing a 3-speed (5-speed?) Sturmey-Archer (or, Shimano) hub ... you would need to have a 700c rim laced to the hub of your choice.

A 3-speed hub may be tedious because each time you need to service the rear wheel (e.g., tyre changes, in particular), you will need to disconnect the linkage (you would also need to do that for forward facing "dropouts"😉 and subsequently readjust everything when it was hooked up, again.

The range on a 3-speed hub is about +30% & -30% of whatever the cog is ... so, if the hub has a 16t cog, then I reckon that the high gear equivalent would be about an 11t & the low would be about a 21t, et cetera ...

The chainring, then, should be based on the respective high-and-low gears which you want to use -- a 42t chainring is common because it was ubiquitous as the inner ring on a Road crank at one time ...

So, choose the combination that works for the type [flat or hilly] of roadway & riding you anticipate encountering.