I don't have ready answers to most of your questions. I can give you some general tips though.
arch/ directory in Linux kernel tree contains various architecture-specific code (not whole kernel for given architecture), majority of Linux kernel code can be used on all architectures. Regarding arm vs arm64 - arm64 refers to new ARM architecture (ARMv8), which AFAIK is not yet very popular, in Tegra-3 you have CortexA9 MP Core, which is bases on ARMv7-A architecture, so you're more interested in "arm" arch sub-directory.
I doubt there's single distribution dedicated to Tegra itself, as Tegra is "only" a SoC - this determines which drivers for interrupt controller, memory, storage, ethernet, i2c, spi, usb, graphics etc. you will need. This is only part of the story, as there are board-specific components, which also affect the kernel image and needed drivers (like the flash layout and other peripherals connected to SoC over i2c or spi for example).
You can download linux sources, and try to configure and compile a kernel (without buildroot - which will automate things for you later on, when you will have a ready configuration and learn how to use it). With Linux you'll have a number of ready board-specific configurations, but usually when porting linux to embedded devices you will want to create your own configuration file which will have all needed drivers (this is probably already done for OUYA and most probably is part of their repo). You can get a lot of information about what's supported in Linux by simply running "make xconfig" or "make menuconfig" and reading help for various configuration options. Just make sure to export ARCH variable so you will get configuration options for ARM instead of your host architecture.
Note that using and creating Linux on embedded is slightly different compared to how it's done on PCs. For PC it's easy to prepare a generic kernel image which will run on most (if not all) of PCs. In embedded world you'll want to have a kernel which is tailored for your board, this also applies to the boot loader. Boot loaders here do what you would expect from typical "boostrap" bootloader which simply starts the OS, but also does pretty much ALL what is done by BIOS in PC (that is e.g. configuring your memory, initializing your CPU, caches, etc. - some things most of people receive for free and usually aren't even aware it happens ;] by simply booting their PC's. That's why boot loader is so important.
Deployment also differs and may be sometimes (depending on hardware) pretty risky without HW debugger. When you're developing your OS, e.g. on a board where U-Boot is used as boot-loader you usually have rootfs image mounted via NFS, and kernel image fetched over Ethernet. When you have your flash image ready with your distro you can flash it using boot-loader (if it has such functionality, U-Boot has), over the OS (if you have one running and properly configured so it allows that) or over JTAG (if you have hardware debugger, appropriate software & hardware (on board) in place and configuration for your board&SoC). I don't think OUYA has HDD btw, most probably you will want your rootfs to be read-only with your distro + some journaled fs NAND partitions for user's data. (But of course it's all up to you as the system designer).
From what I understood from the kickstarter project the authors claim the project is "open" thus most proabably you could try to get some documents from them regarding memory layout, board schematics, flash size, etc. it's usually helpful during development.
Regarding the renderer - I don't know how ambitious your plans are - but there are several "display servers" or graphical environments available for Linux, most popular is X.org which most probably supports Tegra's GPU out of the box (or with appropriate drivers from nvidia's site).
This is long story in general, you'll find a lot of usefull knowledge on free electrons, Internet, books, etc. I think it's too large topic to cover it in a forum post ;].
BTW - Android is actually Linux distro, for a good start you could try to get root there, mount a filesystem with your user-space applications over the network and try to get them running. Maybe even there's U-boot there with shell/console available over UART (getting this done on a commercial-ready product may require some soldering, but if you know someone specialized with electronics and have the schematics of the board, it should be easy to get it done, it's also possible without the board schematics, if you have datasheet of the SoC or a lot of time and patience), so you could start your OS by simply instructing the boot-loader/kernel to boot your OS over ethernet.
EDIT: Sorry for this lengthy wall of text, added some spacing before paragraphs ;-). Found some interesting stuff btw - there are high-res photos of OUYA board here: http://www.ifixit.com/Teardown/Ouya+Teardown/14224/1
which say a lot about the board itself.
There's also a concept document from nVidia regarding how Tegra boots: http://http.download.nvidia.com/tegra-public-appnotes/tegra-boot-flow.html
- it seems it has a boot-rom which does early initialization of storage with actual boot-loader, configures RAM and copies the boot-loader there, and starts it. By taking a brief look at the board layout it doesn't seem there's any other persistant storage there except the NAND flash. Thus if you'll work hard enough to break things on flash you may brick the board (which most probably may be revertable if you get the jtag working).
Edited by henryksienkiewicz, 22 June 2013 - 10:16 AM.