Hebrew was originally written with dots all over the place, indicating which vowels to use , whether ב is pronounced 'b' or 'v', etc. Later, in modern hebrew, they removed this to simplify writing. But it makes learning pronounciation more difficult.
Indeed, ה has an h-sound, and the O is a missing dot/ dots somewhere
The Hebrew letter "ה" is technically equivalent to the English letter "h". If you think about the name "Hannah" you will notice the "h" at the end of the word is silent and the ending sound you hear is the "ah" vowel sound. Hebrew basically works the same way. If you have a "ה" at the end of a word it is silent and yes, it very commonly is accompanied by the "ah" vowel sound but not always.