Those numbers are your overall modifier for that skill or saving throw. They include your proficiency bonus if you are proficient in them, otherwise they are just your ability modifier for that skill or saving throw. They're pre-calculated and listed on the sheet for convenience during the game so that you don't have to add up all your modifiers and Proficiency bonus every time that roll is made.
So if your example Cleric is proficient in Wisdom saving throws and has a Wisdom score of 15, their Wisdom saving throw modifier = proficiency bonus (+2) + Wisdom modifier (+2) = +4, which is the number that will be listed under Wisdom saving throws.
On the other hand, your Cleric probably doesn't have proficiency with Dexterity saving throws, and let's say their Dexterity score is 8. Their Dexterity saving throw modifier = no proficiency bonus (+0) + Dexterity modifier (-1) = -1.
There are other factors that can affect this calculation, such as the Rogue's Expertise feature, but this is the basic calculation that will be used in the vast majority of cases.
You also need to discuss expectations if you haven't already
If you just change the mechanics to better fit the style of play that a highly lethal old-school module is written for, you need to discuss the expectations of this style of play with your players too. If you don't talk about these expectations, all that your players will see is that you've changed the system and made them less powerful apparently for no reason. I would highly recommend having your players read a quick primer on old school play; if you can get past the bias inherent in the document, it's very helpful. Even if you don't have your players read the primer, you can still state the main points and present the reasoning behind you've changed the system. Making sure players know that build is less important, that death is frequent due to lack of caution, and that player skill is rewarded is going to be necessary to support the style of play you want here. Other than this...
Running an LotFP module with 5e is perfectly viable with some conversion work
As long as you convert the module's mechanics over, running Tower of the Stargazer should work fine. The main issues would be hit point inflation (which is sounds like you've covered); the Perception and Investigation skills (which it also sounds like you've removed), and Saving Throw DCs. I'm assuming (based on your question) that you feel comfortable making mechanical changes to both the system and the module, so I don't think this will be a problem for you. One point of caution I'd like to advise on, however, is length of time spent to make a character.
Avoid Lengthy Character Generation
The general expectation of a game like LoTFP is that characters die frequently, and thus, must be created frequently. You'll want to keep the time a player spends out of play due to a dead character as low as possible. A LoTFP character can be created somewhat more quickly than a 5E character, so I'd advise making some of your system changes reflect this. Particularly; I'd say that you should have a list of cantrips and 1st level spells available as handouts for your spellcasting characters so selection goes more quickly, that you either enforce rolled stats or use a standard array for scores to not spend a lot of time on point buy, and that you don't use feats and skills (which it sounds like you've already done). This is just a very quick and dirty method of reducing time it takes to create a new 5e character, but hopefully it will work for you.
Best Answer
Since you are a Dragonborn, you are using the Player's HandBook (PHB). Nearly every one of your questions is clearly explained in various parts of the character creation process, so please read through that. However, I'll give you a broad overview of what those things on the character sheet do to hopefully point you in the right direction.
Inspiration is granted by the DM for playing well, so it's not part of character creation. It lets you take advantage on 1 saving throw / Attack roll / ability check of your choice.
Proficiency bonus starts at +2 and goes up slowly as you level; the bonus is shown in the leveling table for any class. The bonus applies to any ability check / Attack roll / saving throw for which you are proficient in the associated skill or tool / weapon / saving throw ability.
Proficiencies in skills / saving throws / tools / weapons come from your class, race, and background. Some are chosen by you from a selection the rules provide, while others are granted explicitly by the rules. The little dots on the sheet are to indicate proficiency.
Every ability score has a modifier associated with it - for example, 10 grants a +0 bonus while 12 grants a +1 bonus (and the pattern continues with more/less bonus for every even score). Rolling an ability check often comes attached to a skill, in which case the bonus you add to your d20 roll is your ability modifier + proficiency bonus (assuming you are proficient). For example, a Dexterity (Stealth) check if you have Dex 14 and proficiency in Stealth would be rolled with a +4 bonus (+2 for 14, +2 for 1st level proficiency).
Passive Wisdom (Perception) is 10 + your Perception, which is Wisdom Bonus + proficiency bonus (assuming you are proficient in Perception).