Firstly, I think the first step in feasibility would be getting OpenWrt running on one, or more of your devices. This easily allows investigation of 1 and 2, partial look at 3, and some information, including basic graphs of signal strength, and area scans of other wifi networks for 4. 5 is not specific to OpenWrt.
I would definitely suggest running your "security-related" services on another host, which it does sound like you're planning already.
That's probably beyond the capabilities of consumer-grade wireless hardware, in general, as you typically can't get access to the digitized IF, so you won't have the data to be able to do the correlation between the waveforms needed.
Also, most all-in-one routers have challenges with complex calculations, between word size, limited RAM, and very often no FPU. These are mitigated on x86_64 / amd64 devices, as well as, to some extent, some of the newer ARM-based SoCs.
Part of my experiment is to find a way to triangulate users with commodity wireless.
I will try to implement one of the followings: RSSI and CSI based triangulation
or Precise Power Delay Profiling with Commodity WiFi
Regarding the computation part, I'd be happy to move everything on a second host, as long as the throughput of sending the data doesn´t choke the router. (Right now I don't have an estimation of the volume of data)
Assuming I can write software for all of the above, I wouldn't mind putting together my own hardware setup. Trying to run this on commodity hardware is rather for bootstrapping the project. If I could simulate the physical layer well enough, I would use a virtual environment. All that being said, I have very little experience on hardware design and I don't know any virtual environment for those kind of things.
I wonder how modern features like multi-path and beamforming are going to complicate triangulation? I guess as long as the stations them selves do not use beamforming it should work well enough. Assuming stations are immobile would allow you to average your data over long time periods to average out spurious noise...