直通 and 乗り換え: a through service and a transfer
Avoid reading a through service as nonstop or necessarily fastest, keeping transfers separate from the number of stops.
Continuing without changing vehicles
直通, read ちょくつう, describes a through transport service without a vehicle change. この電車は空港まで直通です。 says that this train runs through to the airport.
直通ですが、途中の駅にも止まります。 says that it is a through service but also stops at intermediate stations. 直通 does not always mean nonstop.
Changing vehicles or services
乗り換え, read のりかえ, means changing transport. 市役所へ行くには、バスの乗り換えが必要です。 says that reaching city hall requires a bus transfer.
乗り換えなしで行けますか。 asks whether the destination can be reached without changing vehicles. It checks whether a transfer is required along the way.
Travel time and stops are separate information
直通の便と、乗り換えがある便の所要時間を比べました。 says that the travel times of a through service and one requiring a transfer were compared. It does not identify which is faster.
乗り換えはありませんが、五つの駅に止まります。 says that there are no transfers, but the service stops at five stations. Transfer count and stop count are different.
Is 直通ですが、途中の駅にも止まります。 contradictory?
Show the answer and why
No. Here 直通 means continuing without changing vehicles, which is compatible with intermediate stops.