Most of my problems are with the basic use of Google Chrome while surfing the web, bookmarking and finding bookmarks, etc.
First of all, are you actually using Google Chrome? There is a stock browser that comes with the SGS3. It is not Chrome. You need to install Chrome manually yourself. What does the icon for your browser look like? Does it look like the earth and is it labelled, "Internet"? If so, it is the stock browser. Chrome's icon is a small blue circle surrounded by a larger circle that is red yellow and green.
In general, the bookmarks can be accessed via the menu button. The menu button is the button to the left of the home button below the screen on your phone.
But also problems with understanding practically why my new Android phone is better than my old iPhone.
That pretty much depends on your personal needs. Android provides more control and flexibility than the iPhone. If you want a phone that works exactly like the iPhone, then Android doesn't really give you that. There are things that Android can do that the iPhone cannot. For instance, if you do not like the stock browser and prefer a different browser, you can set that other browser as your default. That way, whenever you tap on any url anywhere, in any app, it will launch that other browser you set as default. On the iPhone, if you tap on a url in your email app, it will always launch Safari even though you prefer Chrome.
It was SO easy learning the iPhone, and I just don't really see the advantages of Android yet.
There is something important that you should understand when switching from the iPhone to an Android phone (or any other one for that matter). Android phones are going to be different. There will be different ways to do things. If you are used to the iPhone, you will find that you will have an adjustment period to learn how to do certain things in Android that is different in iOS. I had some difficulties myself as an Android user and using an iPhone. There were some things that confused me.
In general, long tapping on objects on the screen and sometimes blank areas of the screen will bring up a menu of items that you can do. For instance, long tapping on an icon or other object on your home screen will bring up a menu to do something with that object. Long tapping on a blank area on your home screen will bring up a menu that has other things you can do on you home screen. There is also a menu button that you can use to see menu options as well. The back button (right of the home button) brings you back to the previous screen of an app that you are in.
I kinda need someone to use specific examples to show me what an Android phone can do for me, and not just general stuff , like (admittedly) my original post.
There are many other things that Android can do that the iPhone cannot. Without too much detail on what you need, it is hard to provide you with information that is specific to your needs.
One thing that I recommend is trying alternate keyboards. SwiftKey and Swype are amongst the most popular Android keyboards. You may be having some difficulty adjusting to a new keyboard as it is different. If you don't like the stock keyboard, I suggest you give these two a try.
SwiftKey has the best text prediction I have ever used. It analyses your typing patterns to better predict what you want to or mean to type. I find I type the fastest using this keyboard in landscape mode.
Swype has the best gesture based keyboard. Instead of pecking at each key individually, you just touch the first letter of the word and then drag your finger across the other letters you want to type and then release when you finished typing the word. For instance, if you want to type, "hello," you touch the 'H'. Then without taking your finger off the screen, drag your finger to the 'E' on the keyboard. Then drag it to the 'L' and then to the 'O' and then release. Your finger does cross over a bunch of other keys, but Swype is able to figure you you want to type, "hello." I find that this method of typing is best when wanting to type one-handed in portrait mode.
Android also has what is called widgets. They are extensions of an app that is part of your home screen. The widget can provide some information and/or can provide controls that you can access without having to launch the app first. They can also provide some eye candy if you are into that. For instance, I have an app called TheScore. It provides info on sporting events like the scores and news. It has a widget that can display scores for games on the home screen. There are controls on the widgets that allows me to scroll through each game. Another widget I use controls the sound settings on my phone. When I go to bed, I don't want to hear email or text notifications. I do want to hear my ringer if I get a call or my alarm. Normally, I would have to go into the sound settings and turn down the notification sounds. With a widget, I can just with one tap turn off notification sound and when I wake up, turn them back on with one tap.
One thing about widgets that I find is that like apps, there are a lot of crappy widgets that I consider to be a waste of space. There are a few that I find are excellent. You will have to judge for yourself if you like them or not.
I hope this information helps. Play around with your phone. If you have any more specific questions, feel free to ask them here.