Not sure if this is correct place to ask but… when a player drops from a tournament.. do the remaining rounds in the tournament count as losses for a player in terms of their DCI record ?

Since we're long past the days of Elo, the answer to this doesn't actually matter since a loss doesn't cost you anything on your record (or really show up in any meaningful way). That said, no, you're dropped and counted as not having played, which is important for tiebreakers within that tournament.

No - A player's record is based only on rounds that they participated in, meaning paired against another player or granted a bye.