It's always best to clean from the breech end, but if you want to clean from the muzzle end, simply open the bolt, and then run your cleaning rod down the muzzle. Might be a good idea to put a piece of old rag in the bolt opening so the debis that is pushed out, wont end up in the action. Marlins are very easy to clean from the breech end. Simply open the lever half way, pull the lever screw, remove the lever, then pull the breechbolt out. You can now clean from the breech end.
The same way you would clean any Marlin lever action rifle. These models are of the same design of a Marlin 30-30.
Contact Marlin customer service through their website, and request an owner's manual for your rifle. They are free.
my old trick is baking soda and vinigar that always does the trick
Serial numbers were required per a 1968 firearms act. Marlin .22's produced prior to this were not required to have serial numbers stamped on the weapon and marlin decided it was not productive to do so. Although they did stamp some earlier models they discontinued the practice. My Marlin model 56 made in 1960 also has no serial number.
Go to stevespages.com/page7b.htm and look for the manual.
Move the safety forward to the 'fire' position, then open the bolt. As you are sliding the bolt to the open position, pulling the trigger will allow the bolt to be removed.
about $200 max if very clean
use hoppes bore snake in 22 caliber best i have ever used
$165
See if this helps http://stevespages.com/pdf/marlin_60.pdf
Best to ask a gunsmith for assistance.
using the cleaning rod (which is located under the muzzle) and other applienses