Can a male manifest signs of epidymis-orchitis or chlamydia or gonorrhea 10 years after the sexual contact?

Yes, however... The long term sequelae of gonorrhea, chlamydia, and infections of the testicle and epididymis are different from the signs and symptoms of acute infection. Active infection is characterized by urinary pain and urethral discharge. There may also be no symptoms. Long term, there is risk of urethral stricture disease, infertility, and atrophy of the infected epididymis or testicle.
No. Neither gonorrhea nor chlamydia has ever been found to be carried that long in the male genital tract. In theory it might be possible. But at your age (57) these are rare causes of epididymitis or orchitis; E. coli or other standard UTI-type bacteria are much more likely.