ARIMA requires stationarity, but it generates trends - paradox? If a data set is stationary, does it mean it has no trend?
Can we use ARIMA or AR models if there is no trend in the data? 
If there is AR term, it means that our current value is dependent on previous data, and hence it means there will be some trend as future values are dependent on previous ones. So in that scenario, we should have trend at least in our data if we want to use ARIMA or AR models. 
Please clarify.
 A: ARIMA and AR models can apply to both stationary processes and non-stationary processes. Note that the definition of a stationary process discusses the joint probability distribution. 
So they can't have a 'trend' in the traditional sense (trending up or trending down), but do have a trend of returning to the mean value. (If they didn't, it wouldn't be possible to satisfy the stationarity relationship.)
While they can't have global structure, they can have local structure, because what is preserved is the joint probability distribution. Imagine an 'oscillating' series where the next observation can be predicted to be positive or negative with high probability; that can still be stationary so long as the oscillation relationship doesn't change over time and the oscillation is damped.
A: The base condition to use an AR, MA or ARMA models is that your data should be stationary. If your data is not stationary, to make it stationary, we need to differentiate the data that's what 'I' stands for in AR-I-MA model.
To know the trend component in your data, you need to decompose the time-series data.
Please run the below R-code to understand better.
library(forecast)
births <- scan("http://robjhyndman.com/tsdldata/data/nybirths.dat")

#Converting data into time-series data
birthstimeseries <- ts(births, frequency=12, start=c(1946,1))
plot.ts(birthstimeseries)

#decomposing the time-series data to get seasonal,trend,observed and random components
plot(decompose(birthstimeseries))

#building a arima model
ar.model1 <- auto.arima(birthstimeseries)
ar.forecast1 <- forecast.Arima(ar.model1,h = 12)
plot.forecast(ar.forecast1)

Sources:
https://www.youtube.com/watch?v=Aw77aMLj9uM&index=8&list=PLUgZaFoyJafhB73-1JUTRT0y5u_5fjFCR
http://a-little-book-of-r-for-timeseries.readthedocs.io/en/latest/src/timeseries.html
