Can I replace the permanent filter in my furnace?
You can just order a new filter if that makes you feel better.  There is nothing wrong with replacing it.  However most of the permanent ones can be washed in the dishwasher.  I would look at the manufacturers guide and just clean it - as if something isn't broke why fix it.  I have found getting replacements can be off by a little and cause issues.  But you could always keep old one until you are sure what you ordered works.  I would not leave the furnace without a filter.