French language Q&A Forum

Did a quiz, apparently answered wrong, and am now very confused.

The question: Elle ________ monté le poney de Jérémie et il a été très docile.

I went with "a monté". The quiz says the correct is "est monté".

Going by the Q&A, it seems like my answer was correct.  I am stumped in two ways. 

First, the Q&A says that avoir followed by the past participle is used for getting on a horse. This is a (pro)noun followed by a direct object. The lesson uses the example a "a monté mon cheval". I'm struggling to see why the verb auxiliary would switch based on who owns the horse. 
Second, assuming I have the first part wrong someone how and être is the correct auxiliary, should the correct answer not be "est montée"? The subject is feminine. 

The French don't drink "pintes" because they don't use the imperial system. They drink "chopes". Une chope de bière.

In the dictation the phase "auriez-vous" is not pronounced very well, if not at all, it sounds like " I'll give you"

In the lesson above, the translation is given as "will have been" and "would have been" respectively.  How do I distinguish between them in choosing the right translation?  Thank you