The round function affects how a record, multiply, or insert operation ends when it is synced and quantized. When round is on, it keeps recording your input until the next quantize boundary after you finish the operation.
Play-feedback makes it so the loop fades out according the feedback control even when the loop is in normal playback. Ordinarily it only has an effect during an overdub/substitute, etc operation.
Auto 8th makes SL hazard a guess as to your target tempo, and then based on the loop length automatically sets the # 8ths per cycle appropriately, usually to a bar boundary. This makes further quantized operations make more sense, by not making you set the 8ths/per cycle manually.
Mute quantize (and overdub and replace quantize) just enable them to follow the sync/quantize rules as well (normally they would go into effect immediately).
Yes, the delay mode is independent of everything else, serving as a basic tap-tempo controlled delay effect with feedback. To get out of it, just undo, mute, or start a new record.