What does "real time" signal processing mean?
'Real time' is a concept from computer engineering. A real time system is one that is guaranteed, by design, to execute a function or routine in a certain time T, or less. For example, a real-time avionics system is proven to react to signals coming from certain instruments in a time below a given threshold.

In your case, a more precise description (IMHO) of what you want is a "streaming system". You want a receiver that can process a stream of incoming samples without "dropping" samples; in other words, without its buffer overflowing. The easiest way to achieve that is to provide large enough computing power that the probability of dropping samples is very small.

This property is largely orthogonal to the problem of estimating signal features. Since the incoming signal is random, its features are going to vary. You may need to calculate, or find by experiment, how many samples do you need to process to have a useful feature estimate.

For example, these days most, if not all, transmitted signals have no DC component, so the mean will be close to zero all the time (barring imperfections in your analog front-end). I wouldn't worry about updating the mean estimate very often.

In modulation recognition, in contrast, you may need a few thousand samples, and the processing could take some time. You may decide to do something like gathering 5,000 samples (which in your case would take ~40 seconds), and you may take five second to process them, so you'll be updating that estimate every 45 seconds or so.

As you see, it really varies by estimate, and you'll need to figure out the best number in each case, given your requirements and your processing resources.