1. If you pencil in notes then it doesn't make sense to use Quantization -- there should be no need to Quantize. If you want the notes you pencil in to fall on the bar/beat gridlines [which is what Quantization will do] then just place them right at the bar/beat gridlines as you enter them. In the video you appear to have notes placed at what appear to be random locations in time -- did you you do that deliberately because you wanted those notes to sound exactly where they are relative to the bar/beat grid [though they appear to NOT have any specific timing relationship with the grid], or did you just ignore the gridlines when you dropped in those notes? In other words, is there a musical reason why the notes are specifically placed where they are in the video, and are they in fact placed at specific times RELATIVE to the GB bar/beat grid for musical reasons..?
2. Even though GB isn't highlighting the notes when you select a Region, if a Region is selected and you use Quantization, all the notes in that Region will be Quantized. However, if you have one or more notes selected -- either in the selected Region or in another Region -- then ONLY the selected notes will be Quantized. It may not be immediately intuitive, but that's how GB works..
3. You misunderstood what I was saying. I didn't say you can't Quantize notes when the Metronome is turned off -- you can perform Quantization whether the Metronome is switched on or off. What I said was that if you don't PLAY IN TIME with the Metronome then you won't be able to USE Quantization AS INTENDED -- to auto-correct the musical timing of notes by moving notes that fall A LITTLE off-beat onto the nearest bar/beat gridlines. If the notes -- for whatever reason -- have no relation to the musical gridlines, then Quantization will just randomly move them to the nearest [unrelated] gridlines, which would serve no useful purpose. In the videos you seem to be randomly experimenting with Quantization, without trying to achieve a specific result -- to take a musical performance that was played/recorded IN TIME with an audible Metronome [with notes that all fall CLOSE to the musical bar/beat gridlines] and then automatically move the notes SLIGHTLY onto the nearest [intended] musical gridlines, for tighter musical timing, making the notes line up exactly with the musical grid of the bar/beat ruler.
4. The Quantization Strength option is only present in Region view. There are two tabs in the Piano Roll Editor for MIDI/Instrument tracks -- Region and Notes. Whenever there are no individual notes selected, the Piano Roll display automatically shows Region view -- all notes in a selected Region are affected by Quantization, and the Strength slider is available. But if you manually select an individual note [or notes] in the Piano Roll Editor, then the display automatically switches to Notes view, which does not include the Strength option, and only the selected note[s] are Quantized.