I think the point is to not completely fill the middle pad, rather than not replacing it with leaded. You want rid of the old solder for sure, but then just put a little bit of new solder on it.
Right, if the pads are properly prepped then there is no need to squeeze down the IC in question (which is bad practice)
Generally speaking you want more solder height on the outside pads than on the center pad, if you don’t the IC will float and the outer pads will not make proper contact with the board.
In the case of the P13, you will struggle to get the nice slope from the side pads round the edge as they are slightly higher than the M92 IC, my post earlier was demonstrating that if continuity from the destination was a concern that you should be buzzing out there to verify board contact
I usually skip the middle one because I’m a bit lazy to use the solder wick and I’m usually heating around 425 to 450 regardless. A small dab is what I put in the middle center pad for adhesion.