No, only can SMS.

Yes, bootloader must be unlocked in order to sideload or flash the factory image, please note that unlocking your bootloader will wipe all your data in your tablet.

Please note that there are 2 type of updates you can sideload to your nexus 7.
1. OTA zip file, sideload to update to 4.4 without losing your current data in your tablet.
2. Factory image file which restore your tablet to initial state of 4.4, this will wipe your userdata too, you have to do extra steps in order to keep your data.

Since you downloaded the factory image, I recommend you to use toolkit to do the things for you, it is very easy to use, install it in your root folder of your PC, run it and let it download the necessary files then you are good to go.

Toolkit can be downloaded here.

Use the option "Flash Google Factory Image" and follow the instructions shown in your PC, if you want to keep your data, type "N" when the toolkit asks you whether to format userdata before flashing.

This is old model which has stopped producing long time ago since new model came out.

New model thread is here

Actually the tablet itself is good, but tegra processor and GPU is a big no because not all games in android platform is optimized for tegra devices, I own this tablet before and the gaming performance is just so-so only, for example, asphalt 8 running good with decent fps on Nexus 7 2013 at high settings but running laggy on the old model, better find the new model with Qualcomm chip which provides better support in overall.

Send to Asus Service Center since the battery is not meant to be removable easily to replace ourselves.

7c is cellular version of Nexus 7 while 7 is WiFi version only. Not an upgrade from Google to solve issue.

No need

If you sideload an OTA update zip file, you wont lose any data unless you are going to flash the factory image which will wipe everything.