How wraping funnels after sterilization

That will have to be addressed by your SOP and method. Many labs will wrap the item in aluminum foil prior to sterilizing and then unwrap them once they are ready to be used.

once you place the filter inside the holder, how much surface of the filter is exposed? Any part of the filter is covered by the magnets?

If the filter is perfectly centered there is a ring 2-3 mm wide around the edge of the filter that is covered by the filter funnel/magnet.

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