Your basic 66-block works, essentially, by insulation displacement. When the wire is forced into the clip with the punch tool, the edges of the clip bite through the insulation and grab on to the wire. 110-series blocks do exactly the same thing, though their clips are designed a little differently.
FWIW: Punch blocks don't work well with fine-gauge (24 or higher) stranded wire. The stranded stuff doesn't offer as much physical resistance to the pressure of the clip, so it ends up compressing such wire more than biting through its insulation. This leads to intermittents or opens.
Punch blocks work best with solid wire. Always have, always will.
As to your second question, yes: The clips are parallel across rows in different patterns. The larger 66B4-25 blocks have six clips per row, all connected in parallel across said rows, and can handle 25 pairs (50 wires) each.
The 66M1-50's, aka 'split blocks,' have four clips per row. The first clip on the left is in parallel across the row with its immediate neighbor to the right, followed by an open split down the middle of the block, and then the far-right clip is in parallel with its immediate neighbor to the left.
This split configuration allows such a block to accomodate up to
50 pairs (100 wires).There are other configurations of 66-blocks, most often found in older 1A2 key telephone equipment, but the two I've mentioned are the most common. If you're uncertain about what you're looking at, check the part number of the block itself. It should be stamped into the side, or perhaps on the front between the screw holes.
You're correct in your observation. Punching more than one wire into any clip is a recipe for certain disaster.
The way what you describe works is that each jack is, typically, home-run to its own set of clips on a given block. You then have (on a split block) one remaining set of clips to attach the line to. You would simply loop the incoming pair in and out of the block, hitting all the jack pairs you need to and leaving slack to manipulate the loops later on.
If you have to have more than one set of wires in a given clip, you can get stack-ons that provide additional clips.
It is best to install your own stuff. That way, whoever your phone people are don't have to second-guess any modifications done to their work.
Are you also aware that there is a standardized color code for telephone and telecomm wiring? You'd be surprised how many people don't know that.
Happy tweaking.