https://www.sportsprofi.com/out/pict...6_fireball.jpg

your rear AXLE bearings are 1/4" and there should be 9 of them per side.
contrary to your conclusion, the Cone (inner Bearing Race) only works with the "cone" inwards.
Adjust the axle for zero play and zero "roughness" or you WILL ruin the bearings/cones.
this adjustment may take a few tries to achieve.
you WILL NEED a cone wrench of the 15mm size, and a wrench that will adjust or fit a 17mm size to correctly reset the rear Axle...
as to the freewheel with a zillion little bearing balls in it... you should have NEVER taken it apart. new ones in the 7 speed,13/28 gear range sell for about $15 to $20 new.
next time, if you insist on taking one off of a hub to access the axle bearings.. use this tool instead.
Search: Park Tool FR-1.3 Freewheel Remover
or one of a similar size/fit.
set the tool in a stout Bench Vise, then use the wheel as a lever... "like a bus steering wheel"... turn the wheel counter-clock-wise.