How are Android's notifications worse than the iPhone's? Android's notifications have consistently been regarded as superior. There's a reason Apple straight up copied Android's notifications, Google got this oh so very right.
Calendar notifications are in the notification tray until you dismiss them
I don't know what other "event" notifications you are talking about. Also note that a lot of this is up to whatever app you are using and not Android itself.
Calendar
Calendar notifications are in the notification tray until you dismiss them
I wish. See my post for description of what happens 2-3x per week on my Galaxy S4. I'm using the built-in calendar.
(or whatever other calendar program you want - there's really no need to stick with the built-in if you don't like it)
It's simple, basic shortcuts like this that are the reason I like Android. It does take some getting used to, though, if you're coming from iOS (I made the move back in 2010).
As for your settings maybe you just aren't thinking about the android way, for changing the wallpaper you should probably be pressing the menu button on the home screen much like you would right click on the desktop in Windows.
It's quite frustrating, just to pick one, to figure out where to go when you want to change your wallpaper. Settings -> Display -> Wallpaper. Weird - maybe it's just me but "Display" is not associated with "Wallpaper" in my head. "Display" means things like screen resolution, which device I want the display beamed to, etc. Android is riddled with "not quite wrong but takes a second to remember" things like this.
I told my wife yesterday, "I didn't think it was possible that someone, in 2013, would develop a phone that was worse at event notifications than the iPhone but they've done it with Android!"
For reference, I've only been on Android for about six weeks at this point. I did two weeks with the HTC One, returned that (camera was not to my liking), and went w/ the S4. I like the display size on the S4. I imagine that, if nothing else changes, in two years I will switch back to an iPhone provided that the screen size is the same or bigger.
To me, iOS is better. I miss it.