[RPG] How many starting credits do PCs receive

Hit Dice

Your hit die is located at the top of your class's description page. For a Bard, it is d8. Your hit dice are simply a running count of all the singular hit die you accumulate -- you gain one class-appropriate hit die every time you level up in a class. So, a level 5 Fighter would have 5 (5d10) hit dice. A multiclassing 3 Rogue/2 Sorceror would also have 5 hit dice (3d8 + 2d6). Usually, the hit dice are expressed as the total of the individual pools of dice, so that it's easy to see how many of each die you have. That's important for short rests, when you use them to heal.

The hit dice system seems weird or unnecessary at first (it did to me when I started playing, anyway), but it makes it really easy for a DM to generate an NPC. If I wanted to generate that level 5 Fighter, for instance, I can just roll five d10's, then multiply his Con bonus by five and add that, and I'll know what his total hit points are. That's exactly the same as if a player had levelled up a Fighter to 5 -- it just takes less time.

Temporary Hit Points

This is exactly what it says on the tin. They'll be zero for now, because nobody's cast a spell on you that gives you temporary HP, and you haven't used an ability that grants yourself temporary HP. Subtract from these first when you take damage, if you have them.

Initiative

Luckily, this is a really easy one. It's just your Dexterity bonus, unless you have an ability or item that explicitly states* it gives you Initiative bonus.

*Disclaimer: That's kind of a lie: the Bard's "Jack of All Trades" feature grants a bonus on "ability checks" at level 2. Rolling for initative is a Dexterity check, so you actually get an Initiative bonus from it, even though it's not explicit. Watch out for bonuses to Dexterity checks or ability checks.

Saving Throws

Your class is proficient in specific saving throws. The saving throws are classified by attribute; Strength, Constitution, Wisdom, etc. Your saving throw bonus is just the respective attribute bonus. For the saving throws you're proficient in, you can add your proficiency bonus, too.

Inspiration

This is a special mechanic new to 5e. The gist of it is that the DM can choose to give you points which you can spend for free re-rolls. You can only have one at a time, and it only lasts until the end of the session. Look in your Player's Handbook for details; I believe it's next to the Backgrounds section.

Daggers are melee weapons that have the finesse property. The finesse property allows an attacker to use their dexterity modifier for their attack bonus and damage bonus, in place of the strength modifier.

In this case, the tiefling has a +3 proficiency bonus and a +2 dex modifier, so the attack bonus should be +5 with a finesse weapon, unless there is something missing from the sheet that explains the extra +1 to bring it to +6 such as the dagger being a magic weapon or something. That doesn't appear to be the case here because the equipment for the character is listed on the sheet but something is not adding up correctly, or else I'm missing something on the sheet completely.

As for the piercing damage question, piercing is the type of damage the dagger does. The table in the equipment chapter that details the weapons tells the reader what damage die a weapon uses and also the damage type for the weapon. A dagger does 1d4 damage, and the damage type is piercing. The damage bonus is calculated by adding the attack modifier (in this case dexterity because the weapon has the finesse property) plus any other modifiers to the damage (in this case, none), giving a total of 1d4 + 2.

I'm not certain why the sheet is showing the attack bonus as +6 to hit. All of these sheets seem to have an extra 1 that I can't figure out the source of. If someone finds it, please comment because it's really bothering me and I don't know if I'm just missing something plainly obvious.

I'm leaning towards the calculations on all of these sheets being wrong and chalking it up to an error on the first sheet not being checked and being carried over to every other sheet after. I can see no reason why the bonus is +1 higher than it should be, especially since the spell attack modifier is calculated correctly using the warlock's charisma bonus + proficiency modifier.