To delete a to-do tap into the task > dismiss the keyboard if it pops up and scroll down to the bottom of the to-do detail page > an orange trash can will appear in the bottom right corner.
Competed To-dos can be viewed/retrieved from the completed to-do list. Tap into the sidebar menu > tap on the arrow next to 'To-dos' to present the dropdown menu. Scroll down and tap into "Completed" under "History". You can un-complete a to-do by tapping on the checkmark next to it or delete it indefinitely by tapping into the task and tapping on the orange trash can.