Ok, so I think our wires cross regarding terminology here. We're roughly on the same page. So, when you believe something, you can put some probability on how likely it is to be true. I think we both agree that putting probability 1 is either mistaken or a lie. It is asserting that you're infallible. And I think we both agree that asserting your infallibility is silly. So, to every belief you have you put some probability. If I look at the cat on the mat in broad daylight I will put 0.999, and I'll put 0.99 if it's a dimly lit room or whatever. In any case, despite believing the cat to be on the mat, I admit that I am human, therefore fallible, and I will assign some non-zero probability to the negation, namely 0.001 or 0.01. And here I think we're still on the same page.

From this point I think we diverge, and it's just a matter of definition. I've been referring to that small sliver of probability of the negation of my belief being true as "doubt". So with my definition of doubt, you will agree, there is always some doubt. Sometimes more, sometimes less, but it is always there. Let's refer to my definition of doubt as "schmoubt".

If feel like your conception of doubt is basically when schmoubt reaches a certain threshold, namely where you're no longer comfortable saying you believe the proposition. So for example, we might dim the lights quite a lot, and maybe my schmoubt goes all the way up to 0.4 or whatever, and I no longer believe there is a cat on the mat. I'm pretty sure there's something sitting on something, but my schmoubt for the statement "the cat is on the mat" is too high for me to justify my belief to myself. So clearly you believe schmoubt is real, but you wouldn't call it doubt. What do you call it?

Regarding the funeral thing, I think you need to be a bit more critical of your analysis. It is perfectly consistent to believe in an afterlife but also be sad when someone passes. Because for the time being, you will be separated from them. You will be going at it alone, for quite some time in some cases. And that sucks. It's the same as being sad when your significant other will work abroad for a while. You believe you will see them again, and that this is temporary, but you are sad because you will not be able to enjoy their physical presence for a while.

To keep things a bit on topic: equating the interests of the state of Israel with Judaism as a whole is anti-semitic, and the existence of Israel has by and large made the world less safe for jews, not to mention Palestinians.