Seriously Now

Looking at those three problems seriously.  I'll introduce an answer to each in the form of a quote.

So she says, "Uh-uh, You don't have a challenge, you need a challenge." So now I'm challenged, all right- I'm challenged to hold on to my lunch money because of all the big mooses who wanna pound me, 'cause they think I'm a shrimpy dork who thinks he's smarter than them! But I don't think I'm smarter, I just do the stupid homework! If everyone else just did the stupid homework, they could move up a grade and get pounded, too! Is there anymore coffee?

— Hogarth Hughes, The Iron Giant

Agreed, there are a lot of rules.  The task of learning and implementing them is daunting; there's no use in pretending that you can memorize them all in any brief period of time.  However, you're not meaningfully limited in time.  Yes, your game may be starting Friday, but so long as your players understand that you haven't ingested every rule in the book yet, and that for now you may have to look up a few, you're working on this problem and it should get better.  Say these words exactly.  "Guys, sorry, just feeling overwhelmed, but I'm working on the problem."  Then, work on the problem.  Read the stupid rules.  Not every rule every day, just a select number that you set as a goal for yourself, like you would learn vocabulary words for a foreign language.  You were taught how to do this is school, so you should know how.

Don't think about the size of the task.  Don't contemplate your perceived limitations.  You're quite able to memorize a great deal more than you imagine.  Read a small section of the books, think about it for a few minutes, and then tomorrow read another small section.  Go ahead and read sections you've read before.  Read passages for the sake of reading them, rather than making a plan to read a specific thing.  Pay no attention to how much you've read, or how much you have to read.  That doesn't matter.  Remember that you like D&D. You like thinking about D&D.  All you're doing is reading about D&D.  As you do this, the bits and pieces that you collect will find their way into your game, and you'll realize you don't have to look up things nearly as often.  A year or two from now, a very enjoyable year of learning your limitations, you'll wonder why you ever thought learning the rules was impossible.

Let me show you my plan for sending you home. Please excuse the crudity of this model. I didn't have time to build it to scale or to paint it.

— Emmet Brown, Back to the Future 

The key word here is "time."  Because of time, your game world will be necessarily crude, which is to say that it will be in limited stage of refinement.  If you had a lifetime, you would make the perfect adventure.  If you had eons, you'd make an elaborate game world in 1:1 scale.  Unfortunately, you have the time you have, so present your world, apologize for not having had time to perfect it and move forward.

Your world is fine for what you need to demonstrate.  If you have the capacity to build a model of Brown's elaboration, complete with little unpainted grey figures on the sidewalks, all the better, but it's quite clear from the film example given that scale and paint weren't needed to clarify the plan for sending Marty home.  So, let go of any preconception that your game world is going to be this shiny glistening thing.  It doesn't need to be glorious.  It needs to be functional.

Then, as you have more time, you can build small parts of it to scale, as you're able.  You can paint small parts of it.  You can contribute to the general aspect and feel of the game world or its adventures as best you can.  Meanwhile, you can say to your players what Brown says.  "Please excuse the crudity of my world at this time.  The orcs are heading across the field to your left ..." and so on.  If you will ease the standards you are attempting to meet, to a level that you can attain, you will find that worldbuilding is not nearly so impossible as you've led yourself to believe.

The making of a great compilation tape, like "Breaking Up Is Hard To Do," it takes ages longer than it might seem. You gotta kick off with a killer, to grab attention. Then you got to take it up a notch, but you don't wanna blow your wad, so then you got to cool it off a notch. There are a lot of rules. Anyway... I've started to make a tape... in my head... for Laura. Full of stuff she likes. Full of stuff that makes her happy. For the first time I can sort of see how that is done.

—  Rob Gordon, High Fidelity

This will be the most difficult to grasp, particularly for those who have not seen this film or read the book.  The lesson that Gordon has to learn is the same that a DM must learn:  "It is not about you."  This does not mean your game world is not yours; you've defined it, you've worked on it.  It is definitely yours.  But you cannot make the world for yourself, because you cannot run in it.  This is half the message.

The other half is that when you make the world for your players, you're not making the world your players want.  Like Gordon's compilation tape, you're introducing something through your game that your players cannot predict.  You're throwing a surprise party.  You're making popcorn for your friends before showing them a film they've never seen or heard of.  You're sharing an experience in real time that you've had in your head, or that you had some time in the past.

Free yourself of worries that what you're showing them will be "good enough."  If what you made got your heart racing; and if you're full of anticipation for their reaction when you run; they will sense your eagerness and your anticipation.  These things will give your delivery the verve that it needs; exactly as if you were running over to your friends to tell them Kanye West just went into that Chipotle, right there!  They will see it in your body language.  They will hear it in your voice.  When those things convey your concern for them, and not you, you'll have no problem relaying the moments of your campaign.

This requires a shift in thinking.  Some cannot do it.  They are too embarrassed, or too concerned.  I feel I always had a fascination for show-and-tell.  I wanted other people to like something as much as I liked it.  I attribute my keenness to DM to that.

These things are slowly acquired.  They are meant to be.  There is no reason to worry if they can be acquired, however, because if you apply yourself how you can, regularly, you'll be fine.  If you keep willing yourself to grow, watering yourself and giving yourself good soil, you will grow.

Don't worry about that.  It won't solve all your problems, but you'll find you like your problems. And, when others will recognize you, and call you, a great DM, you won't see it.  You're just playing the game.  It won't feel like you did anything special; and you'll feel that what you do, anyone can do.