New Mac with major permission and disk-write problems

Question

Right, so I'm pretty new to Mac, after getting my first Mac computer (a 17-inch MacBook Pro) at the end of January this year. It's been great so far and I love the thing, but I've suddenly encountered some crazy problems which I'm pulling my hair out over because I have tried everything to fix them, and have had no luck.
I'll try to include as many details as possible, and I'm prepared to bear with anyone who asks me about something I've alrady tried, just so I can get this sorted.
Okay, so first of all, the main problem seems to be with permissions, mostly with disk-write permissions. Any apps that I want to install that required keychain access will no longer install. I enter my keychain password, hit Return, and the dialog box closes without continuing. So I hit "Install" again and it becomes a never-ending cycle of entering my password to no avail. Now, this happens with ANY application that requires keychain access to install. It is not limited to any particular application. I know my password is right because the box closes, and if I enter it wrong, the dialog box shakes because it is incorrect.
Furthermore, it seems keychain access is problematic in other apps. If I want to authenticate something, it will do the same thing as I mentioned before, meaning I get nowhere with the application.
From here, it gets worse. If I download something (anything), then restart my computer, it is still there. As it should be. However, if I delete an APPLICATION (not just any file) OR change preferences for some programs (one in particular that I specifically don't want starting up on.... startup), including through System Preferences>Users & Groups>Login Items, they will not save. This is driving me insane. For instance, I downloaded some free apps from the Mac App Store to try out, but decided I didn't want them. I tried to deleted them from the app folder and succeeded. Emptied trash. Gone. Restart, and.... they're back? So I tried to uninstall them via the Mac App Store, once I found you could do that. Again, it didn't work. Any Login Items preference changes don't stay after a restart.
Originally, none of this was a problem and everything was working fine. The first sign that something was wrong would be Apple Mail often asking for passwords, usually for my Hotmail accounts, saying that they were rejected by the server (but are correct passwords, I get the emails from the accounts, and the passwords are always accepted once I type them in, only to be asked for them some time later on for no apparent reason). At the time, I tried to repair the keychain, tried deleting and recreating the mail account entries and what not, but nothing helped. It still happens, but at the time, it was more of a niggly thing than an outright problem.
I should also mention that I did use BootCamp to install Windows 8 on a small partition, but after I couldn't boot back into Mac (I didn't realise you had to use the Option key whilst booting), I found out that you had to hold the Option key to get back into Mac, then used BootCamp to get rid of Windows. Everything was fine so far. Until I decided to reinstall Windows 8 with BootCamp. This is where things started going wrong. I decided to install a bootloader to make it easier for me to boot between the two systems. I was tossing up between rEFIt and Chameleon, and decided that rEFIt would be the best for my needs. So I downloaded and installed it, which seemed to go fine. Until I restarted. Mac would endlessly load (the spinning grey dots with the Apple logo).
Now, I actually managed to fix this, but I should probably go into more detail. First of all, holding the option key and selecting my Mac partition would allow me back into Mac, and same with Windows 8. At this point, I decided to uninstall Windows 8 to try fix my problems, except now BootCamp was giving me errors. I believe it was something about being unable to unmount the disc, but it may have been a different error. I don't entirely remember. So then I decided to try getting rid of rEFIt. I followed the instructions on the official site but it didn't work. So then I tried deleting the files with root (sudo) access through terminal. Which also failed....
So to the Recovery partition. Booting into Disk Utilities, I repaired permissions, which worked fine, and repaired the disk. I believe I had run the disk repair a few times before to try to fix BootCamp when it stopped working. Anywaym it had worked before, but this time, it said that it was corrupted and could not be repaired. Something about needing to reinstall Mac OS X. With all my files on this computer and currently nothing to back it up with (eventually I will have something to do backups with, but it'll have to wait a few months), I'm not going to do that.
Finally, I managed to delete the rEFIt files through Terminal within the Recovery partition. I ran permission repair and disk repair again to clean anything up. Disk repair gave me the same error, but now I could get back into Mac without holding the option key on every **** boot.
Now more problems had presented themselves. I decided that the lock under Login Items was probably preventing me form successfully changing my startup items. Trying to unlock it did the same thing as I previously mentioned. Type in my password, keychain accepts it, then nothing happens. The keychain settings were already defaulted so that keychain would stay unlocked after authenticated, and all stuff like that. Using "Get Info" on anything has permissions locked and again, I cannot unlock to change them, although looking at a PDF file just now, whilst still locked, it would allow me to add or remove users, so maybe that's not completely accurate. I believe I tended to look at the system folders though, and my name wasn't under ownership, although I don't believe it was meant to be, but I was hoping that maybe that would fix the problem. I guess not.
At this time, I still had my Windows 8 partition sitting around and couldn't get rid of it. I heard of the manual way to do it through Disk Utility. I tried this in Mac OS X, and through the Recovery partition, but neither worked. An error about being unable to unmount the drive. I finally found a way to remove it. Honestly, I don't completely remember how I did it, but I believe it was through a command line, uh.... command. Now I had free space that I couldn't use to expand my Macintosh HD partition back to full size, again with the unable to unmount error. Finally, I fixed this by booting from a Mac OS X installation disc that I happened to have, and using Disk Utility off of that. After that, Disk Utility no longer gave me errors for disk repair.
However, my other problems all still remained. I had written a little list of things I found on the internet for fixing my problems. One solution was to use "resetpassword" through terminal under the Recovery partition, then select Macintosh HD and select "Reset Home Directory Permissions and ACLs". That didn't work until I tried it through the Disk Utility on the Mac OS X installation disc. That worked, and once I was back into Mac, Spotlight started indexing again. However, nothing else had happened.
I should also mention that keychain access isn't completely non-existent for me. Setting up a new WiFi connection worked for me (that is, connecting to a new network), but now every time I connect to the network, I have to authenticate it. However, it does accept my keychain password and eventually connect.
Now, another thing on my list to try was single-user mode, and using "/sbin/fsck -fy" until everything was okay. Well, the first time, it found a bunch of errors, then fixed itself up. Then it was all okay. But nothing had changed. So trying again, I this time used ?/sbin/mount -uw /" which I believe is meant to allow writing access to the drive. Now when running "/sbin/fsck -fy", I had an error. Specifically, "Journal need to be replayed but volume is read-only".
So that's pretty much where I am up to at the moment. It seems to be a poblem with write permissions, possibly among other things. If it was Windows, I might be able to work it out easier, but being new to Mac, I'm still finding my way around. I guess this is a good learning experience, but it's not fun to have to deal with it so early on.
If anyone can help me, I'd greatly appreciate it. I have tried many things, so if you suggest something that I have tried and possibly forgot to mention, I'll let you know, but any help is still helpful, even if only eliminating possible problems/causes/solutions.

Answer 1

Actually you first post is so long that most people just glance at it and move on. To say the least you are very verbose.
Your problem stems from something going wrong with permissions, as you know. How and why that happen is usually a user error of some type.
You can try to repair permissions and see if that corrects it. If not I will leave other options to someone that may know more about the permission system on a Mac.