I did wonder whether it might have been an iPhone. To be honest a lot is to do with what you are used to. For example, I find the One easier to use than an iPhone. I find iOS frustrating when I use it (e.g. helping family members with iPads) because it seems so inflexible and some operations are so long-winded. But I know that part of my frustration is just that I'm used to doing things in different ways. They key to success is learning how things work (and with android there's often more than one way of doing something), rather than just assuming that what you are used to is "right" - I've had to make that adjustment myself more than once!
Personally I'd say it's better to describe what you find awkward rather than just saying that something sucks, because the latter wastes time - people have to ask what it is that sucks before they can suggest a solution. And you don't
have to replace anything, it's a matter of preference. For example, you don't like the look of the SMS app. If you install Chomp SMS then out of the box it looks very iPhone like, which I'm guessing you'd be OK with, though you can change it. Now I was using Chomp previously (except I'd turned the bubbles off completely and was using different coloured text on a black background for my conversations, so it actually looked quite different from iOS), but actually am now using the stock messaging app precisely because it looked different to what I was using before. And if I get bored then at some point in the future I can change it again. So there's no
need to use a different app - it works, and many people are fine with it - but you
can if you prefer something else. You have options
I'd also note that many of the system apps are HTC versions - you'd get different versions on say a Samsung or a Sony. If you really want the pure Android version, you need a Nexus device (though the Google versions of some of these apps are also available in the Play Store).
Launchers: well you can have as many as you want, but obviously only one is needed at a time. I just choose one, usually close all others (if you can't see them in the recent apps then settings > apps > all, select app and "force close") then don't worry about it. In the old days I'd have done all of that "wipe other launchers" stuff, but I've never bothered with the One - the system has enough resources and can look after itself fine, and even if it starts the HTC launcher in the background some time it will just be dormant and will drop out of memory because it's not used. I know for sure that other launchers are not using significant resources on my phone, so don't worry about them. I'd see how you get on with the Sense launcher, and if not then Nova or Apex are my preferred alternatives (they are rather similar in what they can do, both being based on the stock Android launcher, so one or the other is fine).
I guess you mean the "app tray", which I think of as the "app drawer" (so I'll probably use both terms!). This is a big difference from iOS. With iOS all of your apps live one one of your homepages (either directly or in a folder). With android you can do that if you want, but it's optional. You can also have apps which don't appear on any of your homescreens. The app drawer is a shortcut to all of your apps, whether on the homepages or not. Ironically, it's one way in which the android UI is closer to a Mac than the iOS one: on a Mac you can put app icons on your desktop if you want, but don't have to, and you will also have an "Applications" folder in your Dock. Well the "app tray" is equivalent to that Applications folder. So you can just put the most regularly used apps on your homescreens, but have access to the others when you do need them via the app drawer. Some launchers have the option of hiding an app in the app drawer if you've placed it on the desktop, but personally I find that more confusing so never do that.
In fact I'm an extreme case: I don't keep a single app launcher on my desktops. I have shortcuts to folders with my most important apps in a dock, and I have the app drawer for everything else, and only use my desktops for widgets (clock, calendar, music controls, system info, live train timetables, etc). Most people do keep at least a few app launchers on their desktops, some treat it like an iPhone and just cover their desktops with launchers. Some even treat their desktops as artworks and keep them mainly empty. I personally think it's one of the strengths of the Android system that you have all of these options, rather than having to use an approach that somebody else has decided is the best.
Finally, I'm sorry to say I've never used Yahoo so can't really offer much advise on that problem (Edit: but I see that tommo has in the meanwhile!
)