I think most of the confusion comes from two-armed combat.
First of all, on page 195 of the PHB, we have the general description of how any character can potentially fight with two weapons (underline mine):
Combat with two weapons: when you perform the attack action and attack with a
light melee weapon that you hold in one hand you can use a
bonus action to attack with another light melee weapon that you are
holding in the other hand. You do not add your capacity modifier to the
bonus attack damage, unless this modifier is negative.
Neither the war hammer nor the long sword is light, so your player's character cannot use these weapons for TWF at all. Note that the Dual Wielder exploit (PHB p.165) would make this possible, but your player's character does not have this exploit. The effect of the TWF combat style is simply to delete the last sentence on the ability modifier.
So, with a long sword or a war hammer, this PC can make two attacks with its action from the Extra Attack function. If he uses his Action Surge, he can make two more attacks for a total of four.
The longbow and the handgun are not melee weapons, so they cannot be used for TWF either. The longbow gives two attacks on a regular turn, or four attacks with an action surge. The hand crossbow also has the loading property, which indicates (PHB p. 147)
Loading: due to the time required to load this weapon, you can
fire a single piece of ammo when using an action,
bonus action, or reaction to the shot, regardless of the number of
attacks that you can normally do.
Thus, the hand crossbow does not benefit from the additional attack function, which means that the CP only receives one attack during a regular round, or two s & # 39; 39 he uses an Action Surge.
What about dual weapon fights?
If character a) gets the Dual Wielder feat, which would allow him to use TWF with the long sword or war hammer, or b) goes into battle with light melee weapons such as scimitar or short swords, he can:
- Make two attacks with its action using the Extra Attack function, AND
- Make a bonus attack with his casual weapon (this is the TWF bit), AND
- Once per short or long rest, choose to use an Action Surge to perform two additional attacks with the Extra Attack feature,
for a total of three attacks without Action Surge, or five attacks with Action Surge. Note that Action Surge does not give any additional bonus action.
- With light melee weapons or the Dual Wielder exploit, Three attacks (five with Action Surge) OR
- With his current non-light melee weapons, or with the longbow, of them attacks (four with Action Surge OR
- With the crossbow of the hand, a attack (of them with Action Surge).
Not six. And "swings" is not a technical term. Good luck!