I want to do a 1.02+ run and i would like to know: is there any relevant version differences between 1.02 and 1.03 etc? Like, for example, in an older version are there any glitches that newer versions don't have.

The Switch version is generally considered the fastest version because of a couple version-exclusive glitches, but if you're playing on PC, then you'll want to go for version 1.05. It saves a few seconds over the current PC version (1.08) in two places: the Undyne cutscene right before the regular Undyne fight (which can be skipped in all main categories except TPE Glitchless) and the cutscene right before the Asgore fight (which is encountered in all main categories except Genocide). It's worth noting that this time save only exists when the language is set to Japanese.