You need to be patient sir. I need to clearly understand your situation before guiding you do something.
1. As you are already logged in at Gmail using web browser, you can change your password ***** clicking Google logo at the upper-left corner, the page turns to Google home page, then click your email address at the upper-right corner, choose "My account", then choose "Signing in to Google " under "Sign-in & Security" section to change your password.
2. If you put some emails in Trash or Spam folders/labels, they will stay there for 30 days before permanently being deleted.
3. There is three-bar icon at the left pane, you click it and choose "Sent Mail" under "Labels", then you can see your Sent emails in the browser on iPad.
4. Like Point 3, click the three-bar icon to see the Draft folder. You can make draft automatically, all the unfinished emails are saved in the Draft folder automatically.