If the autocorrelation below confidence for time series If the autocorrelation below confidence for time series, does it mean, that there is no sense to you past (lagged) data for the forecasting?
And probably the best result is a distribution mean or median (depends on metric mse or mape).
Example:

 A: The confidence bands give a range in which we would expect sample autocorrelation to vary based on random noise alone, if the data generating process does not include any "real" autocorrelation. As such, your ACF is consistent with no AR dynamics, and the overall mean or median is probably a strong contender in forecasting. This is a frequent finding.
Modern approaches to ARIMA order selection rely more on optimizing information criteria than on inspecting (P)ACF plots, so I'd encourage you to look at auto.arima() in the forecast package for R or similar.
Incidentally, the median is the optimal point forecast for the MAE, not for the MAPE. The optimal point forecast for the MAPE is the (-1)-median, per Gneiting (2011, JASA, p. 752 with $\beta=-1$). You may find What are the shortcomings of the Mean Absolute Percentage Error (MAPE)? useful.
A: It means that with the default 5% significance level your series doesn't depend on it's past, so the true model is probably just the mean, yes. But sometimes for prediction, you don't want the true model, but the one that makes smaller prediction errors, so you might still be interested in modelling the series with it's past.
A: The lag $0$ autocorrelation ($cor(Y_t, Y_t)$) will always be $1$ ($Y_t$ is perfectly correlated with itself) and then lag $1$ autocorrelation $cor(Y_t, Y_{t-1})$ will in general be non-zero but potentially quite small. In your plot the lag $1$ autocorrelation appears to be non-significant which does indeed suggest that $Y_{t-1}$ is not useful for predicting $Y_{t}$.
Another way to verify this is to plot $Y_t$ against $Y_{t-1}$. Any clear relationship between the two suggests that $Y_{t-1}$ is useful in predicting $Y_{t}$.
It would also be useful to see the raw time series so other stackexchange users can see use their experiences to help out
