Car has trouble cold starting

So my car has trouble cold starting. I mean, it has trouble cold starting when it's stopped for like twelve hours.
usually I use the accelerator to give him throttle when starting. Today I was cleaning the engine bay and trying to find the problem, didn't find it. But to test it, I started it without using the accelerator and the car after two seconds of ignition started, but it was very slow, like, the car sound is the pistons and all moving parts work, usually they are really fast, but on that "test" the engine sound was very slow and after two or three seconds of working the engine shut off.
I don't know what it is, usually when this happens, I use the manual pump next to the engine to pump diesel to the engine and I use the accelerator a bit. After turning the key for around three seconds the car starts, the sound of the engine starts going faster as the key is continuously turned and the engine starts.

a few things that I remember about it, would be the oil I am using, I am in Europe and here oils are treated different. We use the thickness of the oil to talk about them. So my car apparently should have an oil we call 5W-40, but I am using 15W-40. W means winter, so basically the oil has a thickness of 15 when cold starting and when the engine is hot can go to 40 of thickness. I think the oil may cause the engine trouble because while the engine is not lubricated the car is extremely loud on the first few seconds.
another thing could be air inside the fuel system. I had a leak a few weeks ago, a tube was not so tight and it had this same problem. I took care of it myself by tightening the tube, but after a week or so the problem came again.
I searched for leaks on the fuel system this morning and couldn't find any.

so I wanted to know what can cause a thing like this. The car has trouble cold starting after many hours stopped, but for example, if I stop it and I turn it on after four hours, there is no problem, only exists if it's stopped for many hours.