My iPhone is giving unexpected, creepy reminders
There are two options that are most likely.

Option #1:

Someone has gained access to your iCloud account and has been adding reminders remotely. If this is the case, you should be grateful that they are just adding reminders as they could do far more. 

Solution #1:

Reset your iCloud password immediately and set up two-factor authentication. 

Option #2:

Someone has gained physical access to your iPhone and either knows the password or your phone is unprotected. 

Solution #3:

Change your phone password to something other than 1234, and make sure that it is enabled all the time. 

Lastly, remove the reminders.