Will this interfere with my trunk seal or brake lights?

No. This is a front lip spoiler mounted to the front bumper assembly. It does not extend into or contact rear trunk components or lighting.

Should I use adhesive or drill through the bumper to mount this?

Check your bumper's existing mounting points first. Most front lips use the factory fastener holes in the bumper plastic — no drilling required. If holes aren't present, surface prep and a quality adhesive rated for automotive carbon and plastic will work, but verify your specific bumper configuration before assembly.

Will this stay stable at highway speeds?

Yes. Carbon fiber is rigid and significantly stiffer than plastic. Proper mounting through factory holes or full-surface adhesive (once cured) keeps the lip secure. Avoid pressure washing the leading edge with extreme force, and ensure all fasteners or adhesive are fully set before highway driving.