The difference is the 'L' in LPG. It turns liquid at a relatively low pressure and takes up much less space then. Hydrogen does not do that, so it has to be stored at a much, much higher pressure. For example, a medical oxygen bottle or a scuba tank has around 200 atm of pressure. For cars, hydrogen is usually stored at 700 atm. And the pressure inside an LPG tank is around 8 atm at room temperature.

I think it is, not sure but it requres bigger pressure and hidrogen is smallest atom that escapes even from high presure tanks.

You can't keep liquid hydrogen by pressure alone and even as a liquid it's volume density it's very low compared to other liquids.

A couple issues have been mentioned, but what hasn't been mentioned is that hydrogen is difficult to store, because the molecules are small enough do migrate through most containers and escape. If your container is made of metal, you also get something called hydrogen embrittlement which breaks your container over time.