How To Learn To GM
There are a variety of resources nowadays that can help you accomplish this. There are also many existing questions on this site about GMing that will point you to more content than you can ever consume.
Watch
In your question, you mention wanting to see more examples of real play. There's a number of ways to do so.
Actual Play Resources
- Podcasts capture the entire play session. There's video podcasts too like on Twitch. See Where can I find actual play podcasts for RPGs?
- Session Summaries (aka Actual Plays, Story Hours, Campaign Journals) usually are severely abridged, but leave out a lot of the cruft. See Where can I find transcripts of actual game sessions? and Where to find game session reports?
- Blogs. There's a million blogs about how to GM. Start with the RPG Bloggers Network. Go to the blogrolls of blogs you like to find more like them. Focus in on blogs about your chosen game(s) and play style(s).
- Play by post forums. If you want to watch people actually play in text, there's a million of these too. Many dedicated sites, specific forums on RPG.net, ENWorld, Paizo, etc. In fact, RP-by-post is very popular even when not affiliated with a proper RPG/ruleset.
- Sit in. There are plenty of other people running games, some in public places like your friendly local game store (D&D Encounters, Pathfinder Society) and conventions. See below under "Play" though, if you're going to the effort of being there you need to stop being a wallflower and get on in and play.
Some games also have better advice sections than others - see What role-playing games have good gamemaster advice sections?
Play
In the end though just watching is not the most effective approach to learning. Watching games is less useful experience than actually being in one. Have you considered playing in those games before running them to learn from other GMs? It's reasonably easy to find other gaming groups, you don't have to abandon yours to play in another. Where can I find other RPG players?
Go to RPG conventions, find games at gaming stores, play on forums or G+ (see also Finding online RPG players for a play-by-chat RPG Campaign?) - just get more experience. The GM was often called the "judge" in the old days, and in the legal world you need to spend a lot of time being a lawyer before you make a good judge. You need to spend some time playing to become a good GM. If you can't think how the players will proceed in a given situation, you need more play time.
Read
There are many books on GMing - see What is the single most influential book every GM should read?
Also try watching/reading relevant genre media. "I don't get how to put together a story" should get its first-order correction by consuming some of that genre and looking at the stories.
Learn
A lot of the problem you seem to be experiencing is pure storytelling. Try How do I get better at narrating/storytelling as a GM? and As a GM, how can I create and role-play diverse NPCs better? Read up on the specific aspects of GMing you feel you're not good at, there's plenty here. Try questions tagged with the gm-techniques tag. Feel free and ask questions here as well about specific aspects of GMing.
There are also a large, large number of RPG forums out there in the world, for every game and type of gaming. If you don't understand something someone posts, you can easily reply and ask.
Do
aka How I Learned To GM
We didn't have these newfangled Interwebs when I was a kid. I GMed almost before I ever played. I did play in a very informal game of D&D in a car on the way to Scout camp, no dice, PvP, everyone had artifact weapons. But other than that, I started out as a GM. I bought a sci-fi RPG (Star Frontiers) without knowing anything about it (I had bought and played a little TSR chit game, Star Force, and was looking for other fun stuff from the same company). None of my friends were interested in GMing and I was in a small Texas town that didn't have conventions or whatnot - life was less mobile and connected back then. So I just read the game books and then ran games for my friends. And I kept running them, and learned from my mistakes and corrected. I read comics and science fiction avidly, so characters and plots weren't that hard to devise. Beyond that, I just learned the way you learn to do anything through practice, whether it's a sport, writing, a musical instrument... How-to's and YouTube videos are cute jumpstarters nowadays, but "Do, and learn from doing" has yet to be eclipsed in being the primary way to actually become good at something.
Fear of "making a mistake" is the dumbest and most paralyzing instinct you can have in life. In a video game you're going to die a couple times off the bat; in baseball you're going to swing and miss a lot before you hit; in baking you're gonna burn some cookies. But you learn through those mistakes. It's fine to do a little reading up ahead of time but the only way to become good, really, is get your butt in gear and do it.
It is fair and you are not throwing imbalance in the game.
Well... maybe a 2,5% imbalance on the long run (the expected value for multiple d20 rolls is 10.5).
In my experience, Perception is one of the most used skills. Also, it is - more often than not - a passive skill (the GM asks for a Perception check). However, the mere asking for a check puts the players on their toes, and metagaming arises even unintentionally on a failure.
Adopting the rule M&M and 4th edition use by default is, in my opinion, an improvement in gameplay: it saves time and avoids metagame.
By letting players make Perception checks when they ask for, and using passive Perception for things that they may not be aware of you can speed up the game and preparation time (for example, you can decide beforehand if the party is surprised or not, according to the Stealth check of their foes).
As a GM, I'll usually go further and use passive Knowledge (whatever) for giving them instant information on the stranger phenomena or monsters that they may happen to encounter and a passive Sense Motive against bluffing NPCs. In both cases I keep the opportunity to let them roll if the player explicitly ask for.
Best Answer
There is a lot to remember and when just starting out with the system, expecting any single person to be in full possession of all of it from the start is unreasonable. That said, adopting only parts of the rules at one time, or just narrating the abilities and results of the professions and aspects you are not prepared to run yet will lead to inconsistencies in the campaign and open you up to the risk of accidentally misrepresenting the flow of the game to the players.
Generate, or have volunteers generate cheat sheets for the specific systems of the player characters. Review these with the appropriate characters when you can. The goal here is to familiarize yourself with the procedures and expectations, while training the player at the same time. Between the two of you, things should go smoothly in play. As sessions progress, your knowledge of the system will grow and your reliance on the player's assistance will lessen. As an added benefit, the player will more quickly become adept at using the character's skills and abilities and can then focus on personality and immersion.
In the early stages balance your sessions to allow for scenes that focus on 1) using specific aspects of the system (start small and get progressively larger) and 2) specific aspects of the setting. Expose yourself and the players to practice with the mechanics, and to interaction with the world and its characters.
Unless you have a huge group, you will not have a full representation of character professions and types at your table. As everyone develops a stronger awareness of the setting, their thinking will likely expand incrementally to include options which they cannot perform, or have not yet seen. If you really are not ready to include an aspect of play in a session or scenario, be prepared to explain why it was not possible in that particular case. Don't rule it out, or just invent a result, build up the background of your tale by knowing what got in the way of that option. If you start out without using magic, eventually the players may wonder why they never meet any mages. The explanation helps make the setting yours, and it builds anticipation for the day the mages do show up.
Build good locations, interesting missions, and compelling NPCs. Encourage well-developed personalities in the PCs with room to grow into the setting and establish roots that may not be obvious at the beginning. Take everything in stages, but start from a solid overview of what the 6th World holds.
The system is daunting at first. It gets better.