MacOS – I’ve lost a lot of the accessory windows from some random app install

It is clear that you are having USER file permission issues. What you need to do is run repair permissions on your user folder which you cannot do with Disk Utility's "Repair Permissions" option. Using Disk Utility only repairs system files.

To repair user file permissions you would need to boot into Lion's built Repair Utilities.

1. Power off your computer
2. Power on your computer and press and hold Command + R until you see the Apple Logo. This may take little longer than usual to load.
3. Once the Repair Utilities loads, click on Utilities on the menu bar and select Terminal
4. Within Terminal, type resetpassword and hit Return. This will open up a password reset utility
5. In this window, select your hard drive (Macintosh HD) and then select your user account from the drop down menu located just underneath your hard drive's icon
6. With your username selected, click on the Reset button at the bottom right of the window. This process may take a couple of minutes to complete. This will repair all file and folder permissions for all files and folders located within your User Folder.
7. Once completed, quit the Reset Password application then the Terminal application, and finally, the Utilities application which will reboot your computer.

Source: Repair User Permissions in Mac OS X Lion

If your disk is encrypted you have to unlock it first:

• diskutil coreStorage list will give you the UUID.
• diskutil coreStorage unlockVolume YOUR_UUID will unlock the disk (the passphrase is the password for your user account)

If you want it to behave like Windows, the only real answer is to simply use Windows. I know that sounds flippant, but you cannot use one operating system and expect to be able to pick and choose it's behaviour based on your personal preferences of other systems.

The maximise paradigm simply doesn't work on Macs, where the ideal is that the function is to set the window size to best fit the content rather than the screen. The point being that the content is what is important, and that stays the same regardless of if you are on a 11" laptop screen or a 27" desktop behemoth. Now we all know that this isn't always properly implemented, but we also know that it is the developers prerogative to do the implementation, it's not a failing in the OS, and given a choice of "one size fits all full screen" that always does the same thing, or intelligent (when the developer adds it) maximising to meet the needs of the content, then I prefer the existing system.

If maximise as per the Windows system makes sense for a given app (bearing in mind that for many, I would say most, it simply does not), then you really want to be looking into the Full Screen options that are provided from Lion onwards, which are further improved upon in Mountain Lion for external displays etc, as this will provide you with exactly what you need, you just have to use another icon. If your app does not support this yet, then there are a number of workarounds like this one for the time being.