Omfg, don't get a PET-scan 'just because'. You would literally have to be injected with radioactive particles. The other stuff, while not necessary, will atleast not kill you faster.
Last paragraph is also massively oversimplified. Getting a 'you have cancer'-speech and treatment for a superslow growing prostatecancer will fuck with your mind and body more than the cancer itself. That's why most health care systems advise against general PSA screening.
PSA sucks, it has both low sensitivity and low specificity.