that is two suffixes.
-iyor (present continuous tense) and -im (possessor??? suffix)
you are correct about the meaning.
(ben) yan-ıyor-um
(sen) yan-ıyor-sun
(siz) yan-ıyor-sunuz
(o) yan-ıyor
(onlar) yan-ıyor-lar
(biz) yan-ıyor-uz
you are right, the i is dotless due to vowel harmony rules
the suffix is "-iyor"
the i can be i, ı, u or ü according to vowel harmony rule.
the rule is as follows
i, e -> i
ı, a -> ı
u, o -> u
ü, ö -> ü