meaning of stationary=TRUE in auto.arima function

I have this data which is residual series obtained from predicted values and observations. original series was a random walk with a very small drift(mean=0.0025).

err <- ts(c(0.6100, 1.3500, 1.0300, 0.9600, 1.1100, 0.8350 , 0.8800 , 1.0600 , 1.3800 , 1.6200,  1.5800 , 1.2800 , 1.3000 , 1.4300 , 2.1500 , 1.9100 , 1.8300 , 1.9500  ,1.9999, 1.8500 , 1.5500 , 1.9800  ,1.7044  ,1.8593 , 1.9900 , 2.0400, 1.8950,  2.0100 , 1.6900 , 2.1800 ,2.2150,  2.1293 , 2.1000 , 2.1200 , 2.0500 , 1.9000,  1.8350, 1.9000 ,1.9500 , 1.7800 , 1.5950,  1.8500 , 1.8400,  1.5800, 1.6100 , 1.7200 , 1.8500 , 1.6700,  1.8050,  1.9400,  1.5000 , 1.3100 , 1.4864,  1.2400 , 0.9300 , 1.1400, -0.6100, -0.4300 ,-0.4700 ,-0.3450), frequency = 7, start = c(23, 1), end = c(31, 4))

and I know this residual series has some seriel correlations and can be modeled by ARIMA.

acf(err[1:length(err)]);pacf(err[1:length(err)])
# x axis starts with zero.
# showing only integer lags here, same plot as full seasonal periods. 
# shows it typically can be fitted by a MA model.

I have attempted following fittings:

library(forecast)

m1 <- auto.arima(err, stationary=T, allowmean=T)
#output
# ARIMA(2,0,0) with zero mean 

# Coefficients:

#         ar1     ar2
#      0.7495  0.2254
# s.e.  0.1301  0.1306

# sigma^2 estimated as 0.104:  log likelihood=-17.65
# AIC=41.29   AICc=41.72   BIC=47.58

m2 <- auto.arima(err, allowmean=T)
# output
# ARIMA(0,2,2) 

# Coefficients:
#          ma1     ma2
#      -1.3053  0.3850
# s.e.   0.1456  0.1526

# sigma^2 estimated as 0.1043:  log likelihood=-16.97
# AIC=39.94   AICc=40.38   BIC=46.12

if we refer to auto.arima's help page we see that:

stationary: If TRUE, restricts search to stationary models.

From the acf and pacf of err we can see that it is to be fitted by an MA model rather than AR, why does auto.arima give me an AR fit?

My understanding is that both m1 and m2 should be stationary, then what's the purpose of this stationary argument?

it's even more interesting now, if we plot the roots of these two models:

the model when stationary=T (m1) is less stationary than m2 if we look at the roots plot, although m1$residuals is white noise.

I can't answer the first question, but regarding the second, auto.arima() can actually generate non-stationary models to fit the given time series. The 'i' stands for integrated, meaning it can use integration. You can transform most (all?) non-stationary models by taking the difference (diff) of each observation from the previous (much like a derivative in calculus), and then transform it back to the original time-series by integrating.

So, if you don't want to let auto-arima() generate non-stationary models, then you use the stationary argument, basically limiting it finding a fit using the simpler ARMA models.