No, for the code files you speak of .. i am suspecting your are referring to design templates.. and for admin no again ... the only viable thing you can transfer into magento is your data base… your products… and perhaps customers..
now as how possible that is ? is; it is , though, that can range from anywhere from fairly easy to extremely difficult. the database is not importable in standard format , the table layout is completely different . so you will probably need to export your product data to a csv file and and manipulate it by some means for import to magento… now again - this can range from simple to months worth of work , depending on your store products and their configuration. magento does not support any category import either . or means of importing products with options. though a few hacks are available around the net or on the boards.. all which still require a some manipulation of your current data. there are also a few extensions available.. they can again help with some things… but by no means is a total instant solution.. there are companies that can do this for you .. and if you are unfamiliar with the process its better to use one. it can take even an experienced databaser quite a while to get everything rolled over.. and in the end there will always be a few bits and peices and problems - including things like stock and status that can not get set right.... related products and so forth.. so in actuality you can be quite sometime - getting a db converted.......
as for the other things .. not sure what you really mean about admin settings..... you are moving out of that admin - so there is nothing to take from there.. and for other code files..i am thinking you are talking about design templates.. - no none of that can be converted or used.. however.. a visual representation of your currents sites design can be built and coded into your new magento template files… basically its the same work as building a new store theme - just you have a visual clue of what you want from the start...... basically a picture..
dont know if that helps…