Learn English – Is the usage “one of the better” correct and grammatical

Like many prescriptive rules of its type, this dichotomy was never actually the tradition.

In reality, bad has always been used as a synonym for this sense of poor. (In fact, bad began to be used this way slightly before it was ever used in the moral sense!)

• According to the OED, the first citation of bad in the moral/value sense dates back to only 1325.
• Bad in the sense of "not of the expected or requisite quality; poor, worthless; deficient, inferior; of a low standard, below par" dates back to 1276. This is cited throughout the centuries and into the present day. It has had a healthy existence throughout Modern English.

As you can see, bad has always been a synonym of this sense of poor. At a certain point in time, some prescriptivists began to advocate for the dichotomy that you describe, but this was never actually reflected in usage.

See also: less vs. fewer.

So, there is nothing wrong with using bad in any of the cases that you have listed here with poor, though one might aesthetically sound better than another for a given sentence.

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.