In transmission line does reflected wave travel on the path before impedance or after impedance?
Statement 1: So, in above case, when we reduce it to simple network
theory and we say that the current will travel thru Path 1 and return
thru Path 2 (which we usually call ground path).

Correct, for low speed analysis we can consider current flowing in a loop: -

down path 1,
through the load R1 and
back along path 2.

We &quot;say&quot; (for the ease of the mathematics) that the current takes zero time to do this. Then it's easy to use basic circuit theories (like Kirchhoff's). But, strictly speaking we are not being absolutely correct.

Statement 2: When we increase frequency such that wavelength is
comparable to network, then also current should return thru Path 2.
But according to first diagram, the reflected voltage/current returns
thru path 2.

No, this is not correct; we cannot talk in full circuit loops any more. What actually happens is that Path 1 and Path 2 form a transmission line (that's the name we use when analysing high speed data transmissions). Even before the signal has reached load R1, current is circulating back to the input source due to the input impedance of the transmission line called &quot;the characteristic impedance&quot; or \$Z_0\$.
If the load (R1) doesn't match the \$Z_0\$ impedance, we get a mismatch of voltage and current when they reach R1 and the &quot;excess&quot; (of both voltage and current) has to be sent back to the source in order to avoid ohm's law being violated. That excess is the reflection; it is both voltage and current.