Catan longest road card question
Yes, you can freely extend the length of your longest road to make it even harder for an opponent to claim the Longest Road bonus from you. The rules talk about how you gain the Longest Road card and how someone else takes it from you; nowhere does it say anything that would imply that ownership of the card prevents you from building roads.
Your own settlements and cities do not disrupt your road in any way, but opponents ones do (see Longest Road in the Almanac, p9).