How exactly does OpenWRT work?
OpenWRT is a Linux distro first and foremost. Source code is available, and you can build it yourself if you want.
Official builds are device-specific, and will generally use whatever format firmware file the default device accepts.
Flashing from default to OpenWRT is generally prety easy. First time might require a special firmware image, but subsequent installs and updates can be done using SSH, TFTP, or the standard web interface.
Is it pretty much a complete replacement for a stock AP/router firmware?
It’s a generic router and access point system. It might not have every feature supported by your device. On the flip side, it sometimes supports many more features than your default, too.
The default web interface is Luci. All of the important, basic settings are editable through Luci, and add-ons are available for Luci integration into non-basic feature like advanced QoS, file servers, or adblocking.
OpenWRT uses the opkg package manager to install, update, and remove packages. If you’re familiar with Debian’s apt-get or Alpine Linux’s pkgadd, it should be familiar. Updates can be performed through Luci, or via SSH.
Will it be fine to use on an AP, or is OpenWRT primarily targetted towards routers?
Using OpenWRT as an access point is a common use-case. Should be fully supported.
Am I limited to only a single version of OpenWRT
Generally, there’s only one supported, active release at a time. Some older devices get dropped, which is why you might see references to older versions. That’s not a good sign.
Once a device is supported, it generally stays supported for a while. As long as there’s someone in the developer community maintaining it, you should see updates across major versions, as well as minor releases.
From personal experience, I’ve taken devices across several major releases without major problems. Occasionally, a major update might require a device wipe. Luci provides a way to export settings, so this generally isn’t a huge problem, and isn’t always needed anyway.
Am I limited to only OpenWRT versions pre-compiled specifically for the MR33?
Not strictly, but the device-specific nature means that all of your devices are recognized and supported. You might be able to flash another version of OpenWRT, but it’s generally not recommended.
If you want something custom that isn’t included in the default build, it’s generally a better idea to start with the default build for your device, and selectively add the features that you want.
For the vast majority of users, this will never be needed. The default firmware is generally very capable. Between minor releases, opkg updates, and the ability to extend the device using extensions, most people don’t need more than the default.
But you do have options if you just feel like tinkering or want to learn more about your device or OpenWRT.
How does performance of a stock firmware and OpenWRT compare for other AP’s/Wireless routers?
Generally better, but not always.
So I’m assuming that OEM’s like Qualcomm and Broadcomm don’t provide the OpenWRT team with official firmwares/drivers for their IC’s
Broadcom is notoriously bad for not proving source for their devices.
Atheros chipsets are probably the best supported - most of them have mainline Linux kernel support. Fortunately, the MR33 seems to be Atheros based, so you should be good on that front.