Yep Mod1 gears will fit Mod1 rack.
Module gears are easy to figure out.
10 tooth mod1 is 10mm diameter when meshed.
However with a rack it is Pi x mod x teeth distance travelled per revolution.
10 teeth 1 rev = 31.4159...mm
You may need something above 15, 16 teeth to allow for that shaft size.
SDP/SI is my first port of call for specs, many places stock their parts.
7mm is a bit of an old shaft size, 6mm, 1/4" and 8mm are more common.
Easy enough to get smaller hole size and drill it out.
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