Much of what you’re seeing is normal for the G12. It uses contrast-detect autofocus, which is generally slower than the phase-detect autofocus used by DSLRs like the EOS 300D.

To improve responsiveness:

• Prefocus on a high-contrast subject area before shooting.
• Try manual focus so the camera doesn’t refocus for every shot.
• Check whether red-eye reduction or AF-assist options are adding delay.
• Use settings that reduce write time, such as JPEG instead of RAW if you’re currently shooting RAW.
• A faster memory card may help with shot-to-shot clearing, though it won’t fix autofocus speed.

If you want to experiment, CHDK custom firmware may offer extra control, but it won’t change the camera’s basic autofocus system.

Phones can feel faster because they often keep focus and exposure updated continuously, and DSLRs are faster because of their autofocus design. If very fast autofocus and minimal lag are essential, a different type of camera may be the real solution.