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.
The Dungeon Masters Guide has a table on p.238 which answers your question directly:
Strength: Opposing a force that would physically move or bind you
Dexterity: Dodging out of harm's way
Constitution: Enduring a disease, poison, or other hazard that saps vitality
Intelligence: Disbelieving certain illusions and resisting mental assaults that can be refuted with logic, sharp memory, or both
Wisdom: Resisting effects that charm, frighten, or otherwise assault your willpower
Charisma: Withstanding effects, such as possession, that would subsume your personality or hurl you to another plane of existence
Best Answer
In a similar format to the previous answer, here's an updated count of spells with saving throws from all official published sources available on D&D Beyond. It’s current as of 14/01/2022.
I am aware of one spell, Nathair's mischief from Fizban’s Treasury of Dragons, which doesn’t list a primary save, but can force either a Wisdom or Dexterity saving throw, depending on the random effect rolled. I have counted it as both, which is why the total spell count here seems slightly lower than it ought to be. It’s possible there are other such spells but there is no easy way to search for them; I believe this list is still pretty indicative of the frequency of saving throws in spells.
I note a significant jump in the number of spells with Constitution saves, but only three recently published spells have them, so this may indicate a previous counting error on my part.
For a list of official sources for spells, and how to find them on D&D Beyond, see this question: What official books contain spells?