I've migrated between many macs over the years, and I've always found that the best way to do it, is manually. Normally I use a firewire cable (but you can also use WiFi, USB, external hard drive, dvd/cd, etc) to hook up the two computers, then just drag over files from one computer to the other.
Mostly everything the average user has on their mac will be found in their user folder (home folder). You can just drag/copy this entire folder over, or you can be more selective about which folders in your home folder you move (for instance, you may not want the Library folder). Then, anything outside of your home folder (Applications, for one) you can drag/copy over if you want.
Unlikely. MA only transfer user files, apps, and any associated files those apps need to run (like Photoshop, which installs things into /Library, and not just your particular user's directory, although it does do that too).
If anything, the only thing you can break are the apps that are being migrated or fail to transfer some of your files (music, documents, etc.).
The Power Saver preference pane is located under /System/ and that is in no way modified by MA. Nothing under the "/System" directory is written to, and that is where the OS (and it's core files) are found (among other places, not openly visible to the end user).
It may be that the settings for Power Saver are corrupted (and those reside in the user's directory, specifically ~/Library/Preferences/).
The best solution, would be to boot using the recovery utility (or safe-mode) and delete the user's directory (e.g., /Users/{your username}) and start migration assistant again once you reboot normally (at which point OS X will take you through the registration process again). Obviously this would delete all the files from that user (music, movies, etc.) so make sure you have backups of everything.
Alternatively, you can log into OS X, create a new administrator account (but don't use your regular naming convention, call it Jonny Appleseed/john, for example) using the System Preference's Users & Groups, log out, and log back in using that new account, and then delete your old administrator account, then recreate it using the same steps you did with the currently logged in account. Once that is done, log out and back in with your newly recreated account, and delete the extra administrator account. This will ensure your new account is set up using the same naming convention your original account was set to (making things easier for MA).
Running MA after that, should transfer all the files over again cleanly without having to worry about somethings getting overwritten or not overwritten.
It is also of note that MA just copies over files and doesn't move them. So all the source files are still there and once you delete the user directory, it'll be a total fresh start.
Best Answer
Your 'get out of jail free' card would be if all you have left to transfer are some simple stand-alone documents, rather than user-specific data, email accounts, browser logins & passwords etc. You could then just network the two together & file-share, rather than migrate.
Each migration will set up a new user account on your new Mac.
Your current stumbling block is you would have to keep generating new names. As soon as you do, it will let you proceed - but don't do that.
Picking this apart manually afterwards is going to be an absolute nightmare.*
Set aside sufficient time to be able to do this in one go & start over. Wipe the Mac & install a fresh new OS. Do the full migration as soon as it asks you, when you're initialising for first use.
You will be considerably better off in the long run.
*Been there, done that, don't ever want to do it again.
The procedure to do a full reset is at Apple KB - What to do before you sell, give away, or trade in your Mac In essence, you want to handle this as though you are going to be the 'next user'.