On Duolingo you will find that Lei, Suo, (Suoi) are capitalized to indicate formal you. Lowercase is simply he/she/it. Such capitalization is far more frequent in official documents than in everyday Italian. However, Accademia della Crusca and teachers of Italian as a foreign language support this distinction, and we have implemented it for pedagogical reasons. Imagine if today was the first day you decided to learn a second language, how confusing it would be to deal with lei (she) and Lei (you)!
They are the same, in context it would be clear whether you were talking about a male or female. It is possible to make a distinction by saying l'amore di lei, her love, or casa di lui, his house, but these are particularly emphatic. You're perfectly safe sticking to suo in most cases.
The gender of the possessive does not refer to who owns the thing. The gender of the possessive refers to the thing, just like any other adjective.
Since "cavallo" is masculine, it takes masculine adjectives, including articles and possessives. It is always:
il mio cavallo
il tuo cavallo
il suo cavallo
il nostro cavallo
il vostro cavallo
il loro cavallo
No matter what the gender of the owner is. Therefore "suo/suoi/sua/sue" can be "his" or "hers".
This is not a human being checking your answers. This is two separate branches of a complicated computer program checking the database and applying a correction algorithm.
Sometimes some answers get left out of the database for no good reason. The volunteer course contributors are ordinary people. Mistakes happen. And sometimes the program glitches.
I took Italian for years in school and studied 'a Roma' -- I'm wondering why Duolingo is omiting the definite article in front of so many nouns. Per esempio (for example), I'd have written "I suoi cavalli bevono l'acqua," with the def. article -- in this case, apostrophe L because 'acqua' is feminine and begins with a vowel. Basically, I was always taught that in Italian, you always say "the" before almost all nouns.