Thank you for contacting us, and I'm sorry for the issue you are experiencing. It sounds like you have access to your mSecure data on at least one device since you are able to make an email backup. If that is true, can you let me know which version of mSecure you are using?
Also, there is no PDF created when an email backup is made, so there is some confusion here. What do you mean when you say you can't open the PDF? What is the name of the file that gets attached to the email backup you create?
There may be a way to get the backup restored on your phone, but before I can know that, I have to know what the name of the file is that is attached in the email backup. If it has .msim at the end of the file name, then you should have no problem restoring the data in mSecure on your phone, and you can do that using the instructions found in this help article: Backup and Restore - iOS
If the backup does not end in .msim, then it's still possible those instructions can work, but it's also possible it won't work. If you have problems with restoring from the email backup you have, let me know where things go wrong, and I'll help.
Here is a screenshot of it. HOWEVER, when I try to follow the instructions and login to msecure, there is no 'menu icon'! Ridiculous
Ok, the good news is you have a backup file you can restore from. Now we just need to get that backup restored. I just looked over the "Backup and Restore - iOS" article I sent a link to in my previous email, but I'm not seeing where it mentions a "menu icon" in the Restore instructions. You already have the backup, so you don't need to go through the Backup instructions, which is the only place in the article where I see "menu icon."
Just for clarification, the menu icon is the icon in the top left of mSecure's screen. You tap that, and the app's menu slides in from the left side of the screen. Again, since you already have a backup, you shouldn't need to do this, but if you were wanting to create a new email backup, simply tap the menu icon in the top left of the screen in mSecure, tap Settings, then tap Email Backup in the Settings screen.
Were you able to follow the instructions under the Restore section of the article?
I am unable to download the app on my new phone because it was originally obtained a now defunct Apple ID which I no longer have access to. Furthermore, if I try to back it up and email myself the document, I cannot open the pdf.