The battery will run down, but very slowly. It should maintain a charge for a long time if it is turned off. The ones we have here show an excellent battery life, even when left on. If your tablet is running through battery while turned off, you might want to return it to the store to have them look at it under warranty.

I'm not aware of any product like that. We also have not heard any problems with our tablets needing to be right next to the router to stay connected. The ones we have here were able to stay connected well over 100 feet from the router. If other devices are able to connect to the router and work where the tablet doesn't, then I would recommend taking the tablet back to the store and having it looked at.

No you cannot text

If you are referring to the RAM status bar at the bottom of the running aps tab the number on the left side gives you the current RAM usage of the running aps and the right side number gives you the amount of RAM that is currently not being utilized by applications.

Depending on the number of aps and what those aps are doing those numbers will go up and down, but will always add up to approximately 1 GB of RAM