Two-handing a weapon in DS3 works a bit differently than in previous games.
The most important change is the addition of Weapon Arts, which, depending on the weapon, can do a great deal of damage, counter, or give versatility to your moveset. In any of these cases, your offensive potential is augmented.
Two-handing a weapon also can allow you to properly equip a weapon you do not meet the strength requirement for, as two-handing will add 50% of your strength towards meeting the requirement.
Lastly, for damage output, there is an increase, but it varies from weapon to weapon.
See this Reddit thread:
Name (Strength Scaling): 1H - 2H (% Increase)
Mail Breaker (E): 32 - 36 (12.5%)
Pontiff Knight Curved Sword (D): 119 - 138 (16.0%)
Hand Axe (D): 99 - 121 (22.2%)
Astora Greatsword (D): 128 - 157 (22.6%)
Irithyll Straight Sword (D): 120 - 145 (20.8%)
Longsword (D): 102 - 126 (23.5%)
Heavy Longsword (C): 107 - 134 (25.2%)
Sharp Longsword (D): 111 - 130 (17.1%)
Raw Longsword (-): 96 - 101 (5.2%)
Broadsword (C): 112 - 137 (22.3%)
Great Club (C): 147 - 185 (25.8%)
Club (C): 90 -119 (32.2%)
Heavy Club: 110 - 140 (27.3%)
Reinforced Club (C): 94 - 123 (30.8%)
Butcher Knife (A): 90 - 127 (41.1%)
Deep Battle Axe (-): 104 - 111 (6.7%)
Firstly, the requirements to wield the weapon is different to scaling. Requirements are clearly defined (usually in STR/DEX) as digits, eg: S - 25, D - 15.
Secondly, scaling works from S through to E, S being the best, E being the worst. The scale goes S, A, B, C, D, E.
Finally, (this is going from the DkS2 values, though I don't see why the DkS3 values should differ too greatly), the bonuses granted from scaling go like this:
- S 140%–200%
- A 100%–139%
- B 75%– 99%
- C 50%– 74%
- D 25%– 49%
- E 1%– 24%
So, if you have a weapon that has an S scaling, you will be granted between a 140 - 200% bonus for that stat.
Again, if you have a weapon that has a C/C scaling in STR/DEX, it doesn't matter which stat you level up, it will still only grant you a 50% - 74% upgrade, regardless of which stat you level up.
EG:
+15 Club, 24 Strength, 2 hands.
◾ BasePhysical: 182
◾ StrengthScaling: 132% (A)
◾ StrengthRating: 76% (effectively 36 Strength because two-handing)
BonusStrength = BasePhysical × StrengthScaling × StrengthRating BonusStrength = 183 × 132% × 76% ≈ 183
PhysicalRating = BasePhysical + BonusStrength + BonusDexterity + BonusChaosPhysical PhysicalRating = 182 + 183 + 0 + 0 = 365
TotalAttackRating = PhysicalRating + MagicRating + FireRating + LightningRating TotalAttackRating = 365 + 0 + 0 + 0 = 365
Source
Best Answer
Each summoned player, or NPC will fractionally increase the health of the boss. I don't know offhand by how much for each summon. You can have up to three summons. Basically, it's there to make sure you can't cheese the bosses.
A great wiki to use for information about the lore, mechanics, etc. of Dark Souls is the Fextralife wiki. I highly recommend checking it out. Edit: Boss damage, resistances, and weaknesses do not change.
Edit 2: I did some looking around on forums and Reddit, and the general consensus is between 10-20% more health per summon. In Dark Souls 1, health was increased 50% per summon, and in Dark Souls 2, boss defences increased.
Edit 3: To answer the second part of your question, when your summon(s) enter the boss room, their health is automatically increased, just like the enemies outside of the boss rooms. The effect stays until either you die, or defeat the boss, no matter how many summons die.