Does this histogram of residuals indicate that the residuals are effectively random? I am studying a univariate and discrete time series. I know that residuals should be effectively random and have a good fit, and should have a bell shape.
Does the plot below suggest that the residuals are effectively random?

 A: Welcome to CrossValidated, Marco!
If I understood you correctly, you are using Least Squares Estimator (LSE) for your regression problem. In order to operate effectively, LSE indeed requires normally distributed residuals. A good way to check this is to have a look at so-called Q-Q plot: you draw the quantiles of your obtained residuals versus theoretical normal quantiles. If you see something as a line in the Q-Q plot - you are done - the assumption of normality is fulfilled.
But I want to encourage you to be careful, you also have to check other assumptions required for LSE: independence of the residuals and homoscedasticity.
Hope it will help!
A: First the curve you have drawn is not the bell you're looking for. Your "bell" should be more like this:

Your histogram-drawn-as-a-bar-chart (yikes! Excel encourages terrible things) looks reasonably close to that.
However, histograms are not a very good way to check for normality of residuals.
As discussed here, on occasions - and depending on your choices for where the histogram bars go, the same set of values might look as different as these:

Just to repeat - that's two different histograms of the same numbers. Kernel density estimates and better still, QQ plots (at least once you learn how to read them) are significantly more informative. If you must use histograms, use plenty of bins and do more than one.
