Is there any way I can get stats related to questions-answers on EL&U, eg. total number of questions asked, questions unanswered, total answers etc. and those relevant to the site itself. eg. number of users, number of user accounts deleted since a specific date and such.
Your one-stop solution is the Data Explorer. You will need SQL-fu for creating advanced queries of your own, but lots of queries have been created by other users already so even with no hacking skillz whatsoever you can grab ahold of lots of data.
However, some of the data you mention can be obtained easier still. It's simply displayed, in plain text, in the corresponding places around the site. For example:
- Number of answers, users, visits per day, questions per day: Stack Exchange network stats.
- Total number of (not-deleted) questions: ibidem, or in the top right corner in the Questions tab on the site proper.
- Questions unanswered: the Unanswered tab.
The number of deleted accounts is not to be found out there in the open, and in fact is unlikely to be in the Data Explorer data dump, either. Account deletions, unlike post deletions, are hard deletions performed by devs. What's gone, is gone.