After you get the longest road card, can you start building on it and still retain the longest road card?
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).
Yes. Once you have the longest road card, the only two ways you can lose it are if another player builds:
- A longer road (has to be at least longer by 1 road), in which case the card goes to said player.
- A settlement along your longest road causing it to no longer be the longest road. In this case the card goes to the player with the new longest road. If no other player has a road that satisfies the longest road requirement (5+ roads), then the card goes back to the bank until a player becomes once again eligible.