Is a Librarian required to make a FPT to determine the PR for the base effects of the weapon, seperate from th e FPT needed should any one damage be done and the second internal damage is used?

Related:

If no FPT required then

A. the PR is just that of the Librarian?

B. It cannot be increased by Unfettered or Push?

Maybe Its just because I'm really really tired after my 12 hour shift last night, but I can't make out what you are asking.

No, it doens't require a test just to get the extra Pen and Damage from Psy Rating.

Ok, Answered.

I have another related question.

Does the minimum damage based on DOS for Attack rolls

 Deathwatch PDF 246 pg. top left paragraph

"For all attack rolls, count the Degrees of Success. The number
of Degrees of Success is the minimum amount of Damage
that attack will inflict on a single dice. If the attack inflicts
more than one dice of Damage, the player may apply the
Degrees of Success from the attack roll as the minimum result
to one dice of his choice.

apply to FPT made for follow on damage from a Force Weapon that does damage to a target?

Purgatus said:

If you mean the psychic damage, not the weapon's damage. Then, no, it only applies to a weapon and WS/BS tests.

 I'm with herichimo. The DoS minimum damage roll applies to the attack made with the WS/BS roll, not to any additional effects triggered during that attack- which covers the psychic channeling. If you wanted to allow the DoS minimum damage rule to apply to the psychic channeling damage using the DoS on the FPT roll… well, that would be the GM's call, I think.

I believe this is covered in the errata. The opposed WP test to charge the sword is supposed to be the Focus Power test (should you use that option), complete with the ability to push and get Psychic Phenom. I read that and shuttered. When just hitting, I believe you just use for full Psy Rating.