1. The fuse holder looks like a fairly generic screw-in cap kind. you might try just buying a generic fuse holder and seeing if you can take the cap off and thread it in correctly where the old cap was. You'll want to check the current value of the fuse from your one with an intact fuse holder to figure out what value fuse to replace the other one with. My guess is that it is a fairly regular 5x20mm size fuse, but you'll need to figure out what fuse current you need.
2/3. I'm not sure I undertstand what you are testing? How exactly are you checking the plug? If you are trying to measure continuity across the plug pins, modern Switch-Mode Power Supplies (SMPS) will probably read open-circuit on a multimeter. It might actually still work fine. A better way to check might be to try measuring if there is voltage at the output on the other side when it is plugged in. Alternatively, if you haven't already, you might simply plug it into whatever you are using and see if it charges/power up...
As for using a 1.5A power supply, the important things to read are the "output" characteristics. It doesn't matter as much what the input current is; the main things to keep in mind when replacing any power supply like this are output voltage, output current, and output polarity. The voltage must be the same voltage as the one you are replacing (in this case 12V DC). The output current rating must be the same
or higher. Lastly, you will want to check whether the output is "center-positive" or "center-negative." These days, center-negative supplies are pretty uncommon, but using the wrong kind can blow up whatever you are using if you aren't careful. In your case, the PSU in the image is center-positive, so you will want to replace it with the same. If the symbol shows the dot in the middle as being connected to a minus sign and the "C" shape as connected to the plus sign, that means it's center-negative and can't be used. If the plus is connected to the dot and the minus to the "C," it is center-positive and you're fine.