1) just drag the blue bar across the timeline. That does not activate trim mode. Although the Stupid Tool may kick in if you have it active – I wouldn’t know as I try to keep it off.
2) Splice In is inserting material from the source monitor into the timeline, either at a Mark or at the playhead (to the playhead UNLESS a Mark is present). Everything after that point will move to the right.
Add Edit makes a ‘cut’ where you are parked. Meaning that you can use it to split up a segment into two or more segments, then move them around. Add Edit does not add footage to the sequence.
3) You may want to find the ‘Extend’ button. You can mark an in or out at the point where you want to extend a shot to. You can then instantly do that without entering trim mode.
4) top/tail is a powerful tool that quickly lets you extract the top or tail of a shot in the TL.