This is true, although it is also true to note that NOx is much more harmful than CO2 (298 times as bad) as it has a radiative effect and takes a long time to break down. Methane is only 28 times as bad as CO2. NOx is a major pollutant and component of smog and is irritating to the eyes and respiratory tract. So although the reduction in NOx and hydroxyl means that less methane is inhibited and therefore an increase in methane, that still looks better than continuing to belch out NOx.
This one is a bit disingenuous. EVs have no emissions and do not increase ground level ozone. There are numerous studies that have found the reverse. However they do "increase" ozone if you measure from fuel generation and tailpipe when compared to ICE cars depending on how the fuel is created. If your country is using coal, oil and gas to make electricity then EVs create more ozone per km than ICE. The answer therefore is to push for more renewables and stop using coal, oil and gas to make electricity. It's also important to note that power station emissions are dispersed around the country rather than being delivered straight into urban areas and primary schools.
https://onlinelibrary.wiley.com/doi/abs/10.1002/cind.818_3.x
But it's more likely that they are making it better, but with some side effects as we are weaned off oil. If we all switch to EVs and renewables the world will have to go cold turkey and will have withdrawal symptoms, but it's still better in the long run than continuing to set things on fire.