Hi, I want to ask about the Fallen Clan's kekkei genkai and how it works in battles.

The Fallen wrote:Shinigami are beings of immense chakra, and they can take any soul they wish with these. While these Shinigami have fallen, and no longer retain the strength they once had, their chakra is still immensely power. Techniques that utilize this chakra are known as catalyst techniques. Catalyst techniques require an extra 5 chakra to active, as all as to either be channeled through the user's catalyst, or have the user's catalyst in contact with the user, or be worn or wielded.

Catalyst techniques gain the following benefits.

• All catalyst techniques gain a +1 when clashing with another jutsu.
  
• All catalyst techniques gain 'Push through', meaning that if they clash with another technique of equal rank, the catalyst technique will "push through" that technique and carry on forwards. However it will still be overpowered by techniques of a rank higher.
  

Does this mean that, my D-rank defensive jutsu, which normally defends against a C-rank jutsu, can now defend against a B-rank offensive jutsu? And, if it's a projectile defense, does it mean the push through effect allows it to break the B-rank offensive jutsu?

Push through won't necessarily apply to Defensive techniques, as when an Offensive technique clashes with a defense tech, the Offensive technique ends. Push through, really only applies to offensive techniques whether they are hitting other offensive techniques, or a defensive technique in which would block more than that Technique (Say for instance you use a B-rank technique, and it clashes with a C-rank defensive tech, the B-rank offensive tech would clash and cancel the Defensive tech and then continue on. Note: this example does not include the normal +1 catalyst techniques are given.)

Also yes. It does mean a D-rank Catalyst technique can defend against a B-rank techniques.

Signed,
The creator of the clan,
Ash