[Nexus 7 (2013) Q&A] droidshadow:
Welcome to Android...

Root is an essential part of the Android experience, especially if you want to use everything Android has to offer. You will not be able to flash custom ROMs without having Root. Now I have Rom Manager Pro and I can tell you that when I first started out with Android that app what a lifesaver for me. However, now that I have a bit more experience with ROMs and Recovery Manager I would urge you start learning how to use your recovery manager. Did you install a custom recovery manager when you rooted your Nexus device? If you did not look into installing TWRP Recovery Manager. You can do everything from that Recovery Manager that you can pretty much do with Rom Manager such as make backups. The one great thing about Rom Manager is that it will identify your device and list some Nice ROM's that are available for your specific device. As for root again, some of the best apps available for Android require Root access. Apps like "complete linux installer" which allows you to put Linux on your tablet. Another great app is "titanium backup" this is an app that you will definitely want to buy the pro version. Support your developers! Titanium backup allows you to make a nice backup of all your apps and your user data. Gotten to level 40 on dead trigger 2? An update breaks your favorite app...with Titanium Backup you could restore an older version of an app and even restore your status within a game such as bringing you back to level 40 in the example of dead trigger 2 that i used...which has cloud but it was an example!

Oh one app you should seriously get for your stock Nexus 7 ROM is "quickboot". Quickboot which needs ROOT allows your to reboot your tablet, reboot into recovery mode, and reboot into the bootloader with just one click of a button. This app will truly come in handy on a regular basis...

Now you asked about ROMs...

Of course we have to mention Cyanogenmod! This is being considered the "Cadillac" of ROM's and seems to be a very favorite choice among people starting out with Android to among the most advanced "power users" of Android.

I have tried "Ice Cold Rom Project" and i like that ROM very much...

Another ROM that I can't wait to try out is the "unofficial" OmniROM Project for the Nexus 7. Now this ROM is supposed to support Multi-Windows. Have you seen the Multi-Windows commercials for the Galaxy S4? Supposedly the "unofficial" OmniROM project has made that available for the Nexus 7 and i can't wait to try it out! I will be flashing this Monday...

Here is a link for that ROM on XDA -> http://xdaforums.com/showthread.php?t=2533936

Lastly...

You mentioned that one of your apps is not working correctly because your device is rooted? While this has never happened to me personally I don't doubt that it could happen but not exactly sure why root access would cause an app to stop working. Here is something you could try...

https://play.google.com/store/apps/details?id=com.amphoras.hidemyrootadfree

That link above is to an app called "hide my root" that one is the paid version but there is a free one just do a search on the Google Play Store. What it does is hides root or blocks root for taking place for a given period of time. If root really is the problem for that app then this might help as you can block root and then try starting the app...

Well congrats on coming over to Android! I think once you get the hang of things you will never go back to the iOS (maybe!). Android is such an amazing project and operating system but it would not be a quarter of what it is without all of these people here on XDA. The people here are what make Android great and what make the open source community great!. Keep playing with Android and don't worry about taking risks with your tablet. If you make a backup of your ROM you can always flash back your stock ROM as long as you can boot into your Recovery Manager. If you can't there is a way to push a stock ROM to your tablet with ADB. It is almost impossible to brick your Nexus device but

still don't make ridiculous mistakes such as not making your backups!

Oh...

Yes you can transfer data from your tablet to your PC in a number of ways. One way is with a USB cable but you need to have the correct drivers installed. Do a google search for USB drivers for your Nexus device and you will find the correct ones you need. Another option that you could use is FTP. The Google Play Store has some great "FTP SERVER" apps which allow you to turn your tablet into an FTP Server. You could then download an FTP client on your PC such as "FileZilla" and log into your Android Tablet and start transferring or downloading files.

I hope this has been helpful for you...

-droidshadow