their is их. It does not have any forms. Generally, 3rd person possessives are the same as the Genitive case of the corresponding pronoun (его, её, их).
I couldn't hear the "s" sound in гость I only heard твой год. I guess my hearing is not good
I guess it was гость but i listened multipl times. They said год, your hearing is fine.
There is no rule that masculine words should not end in Ь. It is still a consonant-ending masculine noun.
Statistically speaking, feminine nouns are the majority amongst nouns ending in a ь in Nominative, comprising almost 70% of them.