1.Use a double arrow for this equation Zn→ Zn2+ + 2e- , it is an equilibrium.

2. If you measure the mass of Zn electrode before and after immersing in solution, no mass difference can be observed/measured. The common simplified model (all books) will say that nothing is changing, this oxidation half reaction must be coupled with a reduction half reaction, to allow e- goes somewhere.

3. But you can also think to the Nernst's equation: after immersion, the Zn electrode will be charged at about E= -0.8 V, thus it accumulates electrons! Consider that the electrode is a sphere (disk/plate) and calculate the charge that must be accumulated to raise the potential at E: Q= 4πεRE

See http://hyperphysics.phy-astr.gsu.edu/hbase/electric/potsph.html

Remember that 1F = 96500 C is the charge for 0.5 mol Zn2+. My rough estimation is that the mass reduction is less than 10-9 g.