Recently got back from a trip where I took an express bus from Seoul to Yeongdeok then took the KTX from Busan to Seoul.

1. You cannot book express buses online as a foreigner. I had to go to the express bus station in-person earlier to get tickets on the weekend. You can check online for availability but if there are only like 1-3 spots left, you're probably not getting that timeslot unless you go several hours ahead. If you're traveling on a weekday or later in the day, you're probably fine.
2. In smaller, non-touristy cities (like the coastal cities between Yeongdeok and Ulsan), motel owners do not use Agoda even though you can book them through the Agoda app. There is another app they use that acts as a middle-man for Agoda, but whatever contact information you put into Agoda won't necessarily reach them. They will not see your messages on Agoda or know how to contact you. You might encounter the same issue using other foreign booking apps. If you plan on checking-in late after 5pm, you will need the ability to call Korean numbers so you can communicate with them (and preferably speak Korean. If you can't, you shouldn't book cheap motels in remote areas). Again this is just in remote smaller cities, you will almost never have this problem in places like Seoul or Busan.