Unless you’re submitting a resume for a job in which physical appearance is important (e.g., an acting or modeling job), you should not include a photo, even a professional photo. Instead, you should send a portfolio separately if it is requested either by the hiring manager or in the job posting.
If you want to make a good impression on people by including a photo on your business card or professional social media (such as your LinkedIn profile), you should invest in professional headshots. A professional photographer will be able to provide a quality image that gives a professional aesthetic in a way that a selfie generally won’t.
No. While a professional photo can be useful in certain professions, something like a simple but striking header design for your resume will be better in most cases because it also showcases your branding and makes you memorable for recruiters, without running the risk of introducing bias.