Learn English – “Whether or not…” vs. “whether… or not”

This isn't a question of right vs. wrong. Rather, you are describing style differences. The sentence "I'm not sure this is right" is elliptical, meaning it leaves out words that have a grammatical function in the sentence but are implied.

The word "that" is often omitted.

In regards to your use of "if." This word is informally used to indicate options. The more formal word to use here is "whether," as in "I'm not sure whether this is right." However, that sentence, too, is elliptical. The full sentence, with the implied words in place, is "I'm not sure whether or not this is right."

Leaving out the implied words is not incorrect. As I said, it's a style choice. If a sentence is clear without the implied words, and if the sentence has an appropriate level of formality according to the purpose and audience, leaving out the implied words is generally acceptable.

I think, in this construction, if is essentially equivalent to although. One can substitute although for if, salva veritate, in the examples given, and in all the examples I can think of.

I might add that this particular if construction is an "aside", often set off by dashes or parentheses in writing, or otherwise almost always by commas. All of these punctuation marks indicate that the tone and volume are low, with flat intonation through the phrase, which is a mark of a part of an utterance that's not meant to be parsed as the main predication.

"Aside" is a stage direction for lines to be delivered not to the other players but to the audience.