Put them on the tabs, away from the required part edges. The final cuts remove the tabs. If you’re making only one, you can simply clamp on the tabs, of course. But a screw-clamped fixture would be better if you’ve several to do. If you’re doing this on a 3-axis machine, it’ll need a few setups. If you can get it onto a 4-axis machine and you have the volume to justify the option to make a fixture to mount it to, one setup is feasible.

Absolutely. Machine the fixture plate with mount holes, maybe even some location dowels at the periphery—better than relying on clamping screws for precise position. That ensures good re-alignment if it’s a 2 stage setup. Use the soft jaws for roughing, then transition to internal clamps or vacuum fixtures for finishing. That way, you maintain the tolerances without adding much cleanup.