Here is a simple antenna design that is effective from 3 to 22 MHz. Based on a resonant magnetic loop, it has high transducer gain (high sensitivity), and also very good directionality. You can build it cheaply from junk box parts.
There's also a premium version of the tiny SA that has a bigger display and wider frequency range, resolution bandwidth etc. I've been thinking of buying that one.
Highly unlikely. 802.11x lives in the 2.4GHz and 5.8GHz ranges which are outside of the stated range of the tinySA mentioned in the article. Occasionally radios will work outside of the stated range with a bit of hacking, but 950MHz to 2.4GHz is pretty far. Software-defined radios (SDRs) like the HackRF One or BladeRF cover the 2.4GHz and 5.8GHz frequency ranges, but at a higher cost.
[edit: clarify the frequencies of the HackRF and BladeRF]
[edit2: Apparently the tinySA Ultra can cover the higher frequencies in certain configurations]
The nanoVNA is a completely different thing - as mentioned in the article also.
The Ultra is more than 2x as expensive (but considering the prices of regular spectrum analysers, still quite cheap for its capabilities!)
[edit2: Apparently the tinySA Ultra can cover the higher frequencies in certain configurations]