Do I keep gear from a dismissed soldier

It's common in military parlance to give a short, unambiguous designation to your enemies. Typically the NATO Phonetic Alphabet is used for this type of designation. In situations where your squad may draw from many nationalities, dialects, or ethnicities with different pronunciations of common words, this reduces the chances that a message will be misinterpreted.

For instance, "tango" is used by the military in many situations in place of "enemy target." Likewise, squads may be given names based on the first letters of the alphabet, such as Alpha/Alfa, Bravo, Charlie, Delta, Echo, and Foxtrot.

The "X" in X-COM stands for "Extraterrestrial" so it follows that when you're engaging the enemy, you're fighting "X"es, or "X-Ray" in the phonetic alphabet.

I just reloaded my game about 10 times trying to figure this out and I have some results. I tested the same 5 colonels, randomly mixing them together in testing, every single one of them was psi gifted, but not every time. It is not determined when the character is created, the fact that the colonel with the lowest will became gifted but only once out of the 10 times points to randomly gifting the soldiers being tested but adding their will score to the roll.

Simply put, if you want your favorite characters to all be psychics it is easy, it will just take a long time, you will have to put them through testing by themselves or with rookies added in and keep reloading until they become psychic then work on the next character. I have gotten 2 out of the 3 as gifted in about half of the 10 tests, but I was not able to garner a 3 for 3.