The Maximum duration for Blessing

Both mods have an effect on Paris (I have yet to acquire the other two) and they work exactly how you described them. Quotes from the Paris wiki page:

• Reload speed mod increases the speed at which arrows are drawn from the quiver after each shot.
• Fire rate mod increases the draw speed of the Paris, allowing you to charge an arrow much quicker.

If you're here from the future, the damage calculator pointed out by Oblivious Sage is outdated as of Damage 2.0. Warframe's wikia site has an up-to-date, extensive paragraph on damage calculation, along with formulas.

The system is quite complex, but the gist is:

• Enemies (and NPCs, and warframes) are made of "health materials" - ie. different types of health, shields and armor.
• Every "health material" applies different multiplier against different damage types.
• When you attack, the final damage within your attack is calculated separately for each damage type.
  • Health is a plain, old health bar. If it's depleted, the enemy dies.
  • Shields is a separate health bar that serves as a protection for health bar. If it's depleted, the damage goes to health.
  • Armor is not a health bar. It adds its own multipliers on top of health's multiplier (cumulatively) and reduces damage the health takes. However,
    • the more armor the enemy has, the more weight armor's multiplier has over health's multiplier,
    • damage types strong against armor reduce that protection (dealing more damage), while damage types weak against armor increase that protection (dealing less damage) - on top of the damage multiplier.