These questions and more can be answered by reading the freely-available basic rules.
However, here are specific answers to your specific questions:
What does it mean for me to be proficient in a skill?
A skill represents a specific aspect of an ability score, and an individual's proficiency in a skill demonstrates a focus on that aspect.
Basic rules, chapter 7.
Does proficiency make my other skills not work?
No, other skills still work just fine.
How many skill proficiencies do I get?
By and large, skill proficiencies are granted by your class, your background, and sometimes your race. Other sources (such as feats and downtime) are also available, but talk to your DM about those.
What does a skill's type (e.g. Wisdom) do to a skill?
Each ability covers a broad range of capabilities, including skills that a character or a monster can be proficient in.
Basic rules, chapter 7.
The ability and possibly your proficiency bonus are used to figure out what you add to a d20 roll when it is called for by your DM.
What are hit points?
Hit points represent a combination of physical and mental durability, the will to live, and luck. Creatures with more hit points are more difficult to kill. Those with fewer hit points are more fragile.
Basic rules, chapter 9.
What are temporary hit points?
Temporary hit points aren't actual hit points; they are a buffer against damage, a pool of hit points that protect you from injury.
Basic rules, chapter 9.
What does it mean to have an advantage on saving throws against being charmed?
For this, read about advantage, read about saving throws, and read about the charmed condition.
I've just started and don't understand how I should choose all the numbers that need to be chosen.
Follow the steps in the basic rules, chapter 1: Step-By-Step Characters.
What do I put in the tiny 'inspiration' box?
When you have inspiration, you can put a one, a checkmark, a heart, a dot, or any other marker to represent having it in that box.
What do the letters next to the boxes mean, like cp, sp, ep, pp?
They mean Copper Piece, Silver Piece, Electrum Piece, and Platinum Piece. Also, gp means Gold Piece. See the basic rules, chapter 5.
What number do I put next to cp, sp, ep, and pp?
See the "Choose Equipment" step in the basic rules, chapter 1: Step-By-Step Characters.
What am I even doing on the third page?
This is for tracking things related to spellcasting, which you may have depending on your choice of class. Read the rules for your class, and the basic rules, chapter 10: Spellcasting to understand more.
"None of my friends play this game (that I know.)"
I would highly recommend that if you can fit it in your budget, you pick up a physical box set called the Starter Set (the one with a blue dragon on the front). Schedule a session to play with three to five friends, choose one player to be the Dungeon Master ahead of time and have them read both booklets before the scheduled session, and then start the session by having the Dungeon Master read the rules booklet to the group; this will take 60–90 minutes, but it's well worth it. This will give the group everything they need to start playing, which will take up the remaining 2½–3 hours of the session. If you all enjoyed it, there's enough content in that box to continue for about three more 4-hour sessions!
