Hello! As the description of this Mod says. "Grants the Mech additional HP when it spawns, which absorbs extra Damage, such as:

• those from back and side hits;
• Double Damage;
• Ability debuffs.

Base Damage is still taken from normal HP".

So, returning to your question:

• "Does it stop Nomad, Killshot, or Slingshot ram damage?" - The Mod takes the Damage if it's directed to the side or back. 
• "Does it absorb the extra damage from Blockhorn's shield?" - Yes.
• "Does it keep Stalker and Brickhouse's damage at normal levels?" - No interactions.
• "Does it stop Bastion's blast shield?" - Yes, if the damage is directed to the side or back.
• "Does it stop Volti's thunderstorm?" - No interactions.
• "Silverthorn's blades" - Yes, if the damage is directed to the side or back.
   

Thankyou :)