Stable Android version with a gallery for Nexus 7 2013 So I got a Nexus 7 2013 tablet recently for my sister. Upgraded it to Android 6.01 (which is the last OTA upgrade available). My sister didn't like it for the reason that there is no Gallery. She was a heavy Gallery user in her earlier tablet. Other than that it worked fine for a few weeks. Yesterday, it went into the circles loop - https://i.pinimg.com/originals/27/03/92/2703922d465e0d968762093b2c1443df.gif - this animation kept going on &amp; on &amp; on - in between it would say updating app 16 of 16 &amp; then again the animation starts again.  

I am thinking of doing a factory reset - I assume factory reset would take it back to the 4.x version it came with. Post that I want to upgrade it again but to some version lower than 6.01. 

Which is a good stable version before 6.01 which also has the gallery which I can update to?
Factory reset does NOT take the device back to 4.x - you'll stay on 6.0.1, and you might not even escape the bootloop if it's caused by something wrong in /system.

What you can do right now is to flash any factory image via fastboot (you can arbitrarily downgrade this way). But although this is almost guaranteed to make the device work again (unless the device is broken hardware-wise), an early Android version will render some modern apps compatible, and leave you vulnerable to a great number of security risks.

Although not necessary for your intended purpose, the ultimate way out is to flash a custom recovery then an actively maintained custom ROM. This will bump your Android version to the latest the community has to offer (up to Android 8.0.0 as of now - do note that the latest isn't necessarily stable or bug-free), and by flashing updates to the custom ROM, you will be patched against vulnerabilities in time. Get familiar with the basics and find the resources at XDA-Developers.

As for your purpose - using a gallery app - stock and stock-based ROMs should have Google Photos by default (not sure why yours didn't, you probably simply missed it), while other ROMs usually have an alternative one, which loses the sync-to-cloud feature but brings a cleaner, no-network-needed experience.