Pad size of power jack

If you're interested in solderability and manufacturability, then you should follow the recommended pad layout. I've never had a manufacturer's recommended pad layout give me grief, although I have run across a few vendors whose dimensioning requires a fair bit of headscratching and pencil-and-paper chicken-scratching in order to figure out offsets and spacing.

You are making some bad assumptions in your calculations though. No, pins are not often centered on the pads "lengthwise" but they are often centered widthwise. Y1 and C1 would most certainly be given by the manufacturer. The recommended land pattern will (in my experience) give more space for the pin on the "outside" of the pad and less underneath it. My guess is that that gives a good shape to the solder connection. You won't have anything in terms of heat dissipation unless there are a lot of grounds or you have a ground pad underneath. In the case of a lot of ground pins, you'll want to give them a lot of copper fairly quickly, but you'll want to connect the pad to the copper with thermals or you'll have soldering problems.

I wouldn't worry about minimizing board space, especially if you're not building a million of these. The half a millimeter you might save by shaving Y1 a little isn't worth it.

It depends very much on how the boards will be assembled and soldered. If you are doing it manually then it will not matter too much. I try to pick a slightly larger footprint for my DIY boards because that makes it easier.

If the boards will be professionally assembled then the footprint will definitely matter. There are often slightly different requirements for e.g. reflow soldering vs. wave soldering. This is when you'll need to work closely with the assembly house to work out what size and tolerances they can work with.