Yes, you can email the corresponding author. They may or may not receive or read your email, but there isn't much you can do about it.
No, you do not need to stack credentials. Even mentioning them at all, especially in the beginning of your email, probably makes it more likely it will be thrown away than read. You will sound like a crazy person if you mention all sorts of credentials. It's fine to have a brief signature at the end of your email; my professional signature has my name, degree, and work contact information.
They probably won't take your advice, and you shouldn't wait for or expect a response. Papers are published so that everyone else can use the contents. The person publishing a paper doesn't own or have responsibility for all the subsequent steps that might be taken. Someone else (including yourself) is free to make that modification and publish their own paper or use it for their own devices.
To have the best chance of having some positive impact, write directly and concisely. Spend far more time revising your message than writing it initially: make it as short and simple as you can. A brief greeting of praise is fine: "I was enjoying reading your paper (title)..." is enough. A paragraph of how much you admire their work is far, far too much.
Write from a serious email source; .edu is probably ideal, but if you aren't affiliated with a university you probably don't have an .edu address. Hopefully you have a professional email you'd use for resumes and such, rather than "firstname.lastname@example.org". Use an informative but brief title.