You can use the process Events > Combine stim/response to recombine/match some specific stimuli with some specific responses (and create "correct" and "error" events?). Read the help directly in the process options. There are other recombination processes you might try.
Also is it possible to extract the time (in milliseconds) from the presentation of the second stimulus until the response
If you right-click on the "link to raw file" > File > Export to Matlab, you'd get access a direct access to the events structure. If you have the same number of events in the two categories "second_stim" and "response", you can subtract the "times" value of the two directly to get the response time.
To get matching event categories you can directly subtract, use grouping/combining processes.
The structures of the events is explained here:
https://neuroimage.usc.edu/brainstorm/Tutorials/EventMarkers#On_the_hard_drive