Can I run V2 Chemistry data with TPv3 or vice versa?

No, you should not run V2 chemistry runs with V3 pipeline. Tapestri v3 pipeline has been optimized with Tapestri core kits v3.  Likewise, Tapestri Pipeline v2 has been optimized with Core kit v2 chemistry. Analyzing v2 data with the v3 pipeline (or vice versa) is not supported.