Transactional emails, such as confirmations, are not going out
CiviMail isn't responsible for anything other than Bulk Mailouts.

There are Scheduled Jobs required for things like Scheduled Reminders which you can find at civicrm/admin/job?reset=1

In case you hadn't spotted, there have been two SparkPost extensions released. the other is here. Not suggesting either is better, or even how relevant it is to your issue

If you just click 'Send Email' via Actions on a civi contact record, does it get sent?

And what is the outcome from send a Test Email from /civicrm/admin/setting/smtp?reset=1