How can I generate reasonable dummy/artificial data from a pre-existing time-series data?
This problem is referred to as scenario generation, commonly used in stochastic optimization. The key problem is that you have to respect correlations among the different variables, which means that you need to model the joint multivariate predictive distribution. One way to bypass this is to use Copulas, which only require modelling the marginal probability densities. An approach widely used in engineering is the following:

Model the marginal (empirical) probability distribution of each variable separately. You can also model the conditional probability distribution using probabilistic forecasting if needed.
Estimate the empirical correlation matrix between the time series.
Use the empirical correlation matrix and the marginal conditional distributions to fit a multivariate Copula.
Obtain correlated scenarios by sampling from the multivariate Copula.

I am including a standard reference from the field of wind forecasting, which models the temporal correlation from the same time series. This can be applied to the case of different time series (spatial correlation).