I agree!

For me, I often use "I'm sure that" as a way of making the conversation more casual. If I'm talking with my friends or coworkers, I'll use that as a way of leaving room for their opinion and to make what I am saying sound more friendly. Jonathan is also right. The way in which we say things conveys a lot of meaning.

I agree with you. It's such a difficult one to explain though to a non-native speaker. And anyone who learns another language knows this exists in all languages. It is such a nuance that I do wonder if it can ever really be grasped by non-native speaker. But also something you didn't mention here is the intonation of the voice. This plays a big role in the meaning as well. For example if the speaker says" "He's joking!" in an excited voice then it could mean he isn't. I think that in all 3 of these examples you give the intonation would change their meanings.

You would only say “I am certain exc…” if the credibility of the topic was being questioned. I would say that the phrase “I am sure exc…” definitely shows less certainty then “I am certain”, but it is also really only used when the credibility of the topic is being questioned. So, they are used in different scenarios, but I agree that saying “I am sure” is pretty counterintuitive!

I agree. One of my pet peeves is that news commentators and politicians often start their sentences with "I think...." For example, I think that we need to do something about the border crisis. When they start with I think, they are just expressing their opinion, which may or may not be accurate. If they are confident, they should just say, "We need to do something about the border." Even saying "something" is an empty phrase that doesn't really mean much.