I think it depends on where you learn Spanish. It's used a lot by the Central Americans near me and all of my South American teachers
"Estoy cierto" I'm certain
"Soy cierto" I'm certain but with a bit more emphasis
"Es la verdad" Is the truth
"Es verdad" Is true
"Estoy seguro" I'm safe
I noticed you made a slight mistake in English. English speakers almost never say something "has no sense" unless you are referring to a person. For example, "He has no sense." However, we commonly say that something OR someone "makes no sense". (When referring to a person, "makes no sense" has a slightly different meaning than "has no sense".) For example, "This idea makes no sense." If you have any questions, you can ask me or any of the other native English speakers on Duolingo.
I wrote "besides, that's not true" - and it marked "that" as an error. I am not an English native speaker (I am Italian and I have to take the Spanish course in English, since it is not available in Italian), but I thought in this case "it" and "that" could be interchangeable. Could an English native speaker tell me what is wrong?
This can get tricky. If a fact is known (for sure known), then a conflicting statement is generally false. However, many times, something may be suspected, or commonly thought to be true, or sometimes true. In these cases, one might challenge such an assumption, and say it's not true, or not necessarily true, or not ptoven to be true, but that state wouldn't make the statement false.
I liked this one. I wrote "she is not sure" and it marked it as incorrect. Then I realized if it was talking about a human and its feeling, it should have used "esta" instead of "es". So by using "es", it tells us about the permanent aspect of a thing-its truth. Am I right? I feel I spoke so vague. :p
Tried "what's more" for "además". Not accepted. Think it should be (see https://www.spanishdict.com/translate/what's%20more). Reported.